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find the derivative of y= 10^(x^2)

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I. Find the derivatives of the following functions. (a) y = ln(2x …

Given y = −x2 + 4x + 1 and y(3) = 8, find y. (10 points). Answer: … Next we test these numbers with the second derivative: f (x)=3×2 + 2x − 2. … http://www.math.ohio-state.edu/~cosmin/teach/132/solmid2wi00.pdf
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I. Find the derivatives of the following functions. (a) y = e (5 …

Hence y = −x4 + 6x − 3. IV. Find the following integral. ∫ (x + 1)2 dx …. (10 points). (a) Use the second derivative test to find relative max and … http://www.math.ohio-state.edu/~cosmin/teach/132/solmid2wi01.pdf
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Evaluating the Derivative of a Function

get y = u.v, where u = 5×2 + 3x and v = x4 + x. du = 10x + 3 and dv = 4×3 + 1 … where u = x2 + 1 and v = x3 + x2. Now we have y = u v. Find the … http://www.tlu.ecom.unimelb.edu.au/pdfs/maths/Evaluating_the_Derivative_of_a_Function.pdf
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Math 30 Date: Derivative Gateway Test Name: Find the derivative of …

Find the derivative of each of the following functions. Do not simplify your answers. …. 110. y = x2√1. − x. 4. 122. y = xebx, where b is a constant … http://www.math.sjsu.edu/~hsu/courses/32/morediffreview.pdf
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1. (10%) Find the derivatives of the following functions by …

(Hint for (ii): G’(x) is in terms of / and G). 6. (10%) (a) Find all numbers … third derivative. The dashed lines are tangent to the graph of y — f(x) at … http://www.lib.ntou.edu.tw/exam/biofish/94/1.pdf
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(4 points) White version: Find the derivative of ln x3e2x (x + 1 …

17 Nov 2009 … with y = x3e2x(x + 1)5/3, computing y with either the quotient rule or product rule. … Pink version: Find the derivative of x3/7e. −x. (x − 1)5 … (x3 + 3×2)ex(x + 1)5/3 − 5. 3 x3ex(x + 1)2/3. (x + 1)10/3 … http://www.math.vanderbilt.edu/~schectex/courses/f09/Answers/QUIZ4.pdf
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Math 160. Practice test 1. Name: Problems 1-3: Find the derivative …

Problems 1-3: Find the derivative f (x). 1. f(x) = x2 + …. The equation of the tangent line is y − 2 = 1. 4. (x − 4). 10. limx→c f(x) is undefined at c … http://www.utm.edu/staff/mharvey/160/160practicetest1a.pdf
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3.1 Derivatives of Polynomials and Exponential Functions Let’s …

Example: Find dy dx for x2 + xy = 10. Then, find dy dx when x = 2. … Example: Find the derivative of y = (sinx)x2+3x. Where does e come from? … http://people.southwestern.edu/~marra/154chapter3.pdf
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Summary of Rules for taking Derivatives

You know that the derivative of x2 is 2x. Then the derivative of 10×2 …. then simply take each term and find its derivative with respect to y, then … http://www.karlscalculus.org/pdf/divrules.pdf
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Calculus I Practice Problems 2 1. Find the derivative: f x)=/ x + …

2. Find the derivative of f. ( x) = x2 + 1 x + 1. 3. This graph is that of a function y = f. ( x) . Sketch the graph of its derivative. -10 … http://www.math.utah.edu/online/1210/Practice_Problems/Probs2/Probs2.pdf
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Calculus I Practice Problems 2: Answers 1. Find the derivative …

Sketch the graph of its derivative. Answer. Here is the graph. -15. -10 …. 7. Let y ¢ x x2 ¦ 1. Find the equation of the tangent line to the graph at the … http://www.math.utah.edu/online/1210/Practice_Problems/Probs2/Probs2ans.pdf
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1. The graphs of the derivatives of F(x) and G(x) are given. For …

Find the volume of the object formed when the region bounded by y=x3-7×2+10x, x=0 and x=2. (graphs below) is rotated about the x-axis. … http://www.math.upenn.edu/ugrad/calc/m103/exams/Math103F06.pdf
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MATH 2200, Fall 2009 Exam 1 (1) Find the derivatives of the …

(2) Use the definition of the derivative to find the derivatives of the … y − 7 = 10(x − 1). (b) f(x) = 1 x at x = 3. Solution We first find f (x) via … http://www.math.uga.edu/~dkrashen/courses/2200Fall2009/exams/practiceExam1Solutions.pdf
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1. (a) Find the derivative of the function f(x) = 1 x +2 cosx+3 …

region on the x − y plane that is related to the curve y = f(x). … (b) g(x) = x + 1 x2 + 1 . (c) p(x)=(1+ x4)10. (d) q(x) = sin ( 1 … 2 x. + 3 cosx +. 4. √1. − x2. +. 5. 1 + x2 ). (d) Find the derivative of the function F(x) = ∫ … http://www.pitt.edu/~sysoeva/math220/finalSamples/m220finalSample7.pdf
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Math 140-02 Sample Exam 2 1. Find the derivative of y = 4 cosx 2 …

Find the derivative of y = 4 cosx. 2−cosx. 2. f (x) = x4 −8×2 … 9. Find (x2 −5x)4 (2x −5)dx. ∫. 10. Find x2. (x3 + 5)4 dx. ∫. 11. Find. 3x x2 −1 … http://www.math.wsu.edu/faculty/schwartz/math140_sp09/sample_exam2.pdf
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Derivative Computation Question Bank

2. Find the second derivative of y = xp(xq + a) + bÏ€2. p = 3..5 q = 1..4 a, b = 1..10. Topic 3 — product rule. 1. Suppose f and g are functions of x, … http://www.math.unl.edu/~gledder1/EDU/UNLQB_derivative_computation.pdf
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Sample Questions Derivatives

y = x1/x. Question 18. Use logarithmic differentiation to find the derivative of y = (x3 + 10x − ln x)3. √ sin x − 2x. (tan−1 x + 1)3/2 … http://www.nevada.edu/~cwebster/Teaching/HON181/differentiation.pdf
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3.6 Derivatives of Logarithmic Functions 1. Overview

+ 2 cot x. 2.) Find the derivative y of: y = √ xex2. (x2 + 1)10. This is a very nasty function. It is the product of three functions. √ x, ex2 … http://www.math.umn.edu/~decel004/calculus_notes/3_6_derivs_of_logs.pdf
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Calculus – Gil Strang

In 1-10 identify f(y) and g(x). From their derivatives find -. …. In the first case, solve for y = 2/x and take its derivative: dy/dx = – 2/x2.The curve … http://ocw.mit.edu/ans7870/resources/Strang/Edited/Calculus/4.1-4.2.pdf
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Chapter 4 The Derivative

Sketch the graph of a function f(x) whose derivative is shown in Figure 4.1. …. 10. 12. 14. –1. 1. 2. 3 x. Figure 4.10: Figure for Problem 4.18 … coordinates to find. (2,3) x y. Figure 4.12: Figure for Problem 4.21 … http://www.ugrad.math.ubc.ca/coursedoc/math102/keshet.problems/chapter4Problems.pdf
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Michael W. SI Math 165 1. Find the derivative of f(x) = ax + b cx …

sin(x) = 1. 2 when x = Ï€. 6 or x = 5Ï€. 6 . 4. Find the derivative of f(x) = ( x2 − … if x2 tan(y) + y10 sec(x)=2x. So using implicit differentiation, … http://www.dso.iastate.edu/asc/si/documentdb/spring_2008/MATH_165_All_Instructors_mwest_SI165_1_ANS.pdf
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Avoiding some common derivative mistakes

Find the equation of the tangent line to y = x2 at the point (1, 1). … x2 ln x = 2x ·. 1 x. = 2. What’s wrong? 10. Find the derivative of f(x)=8×3. … http://www.math.uiuc.edu/~mbarrus2/math220u1/CmmnMstksWksht.pdf
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DCU School of Mathematical Sciences BASIC SKILLS WORKSHEET 10 …

We write this as y = x−2 and apply the rule to get …. Find the derivative of each of the following functions. (a) y = 4×9 − 5x + 12 … http://www.dcu.ie/maths/mlc/basic skills 10 derivatives.pdf
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1. (12%) (a) Use logarithmic differentiation to find the …

y − Ï€. 4. = x. 2 . 2. (10%) Find the highest and the lowest points of the curve given by x2 + xy + 2y2 = 28. Sol: First note that the curve is an elliptic … http://www.math.ntu.edu.tw/~cala972/grade/971A2midsol.pdf
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Derivatives of Exponential Functions

Find the derivative of each of the following using the rule found above. (For some, … y = 10x y = 4 · 3x y = 42x y = (1/2)x y = 3. 5x y = x2 + 2x + 2 … http://staff.imsa.edu/math/prof-dev/calc/ExpoDeriv.pdf
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Math 105: Review for Exam I – Solutions Basic Derivatives Basic …

(b) Using the limit definition of the derivative, find f (x). f (x) = lim … Thus, 8 = 10 · 2 + b, so b = −12 and we have y = 10x − 12. … http://abacus.bates.edu/~etowne/020806towne105reviewsoln.pdf
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Math 101 Spring 2008 Practice Test 1 Solutions 1) Find the …

2) Use the limit definition of derivative to find the derivative. …. line is y = (1 + e. 2. )x − e. 2 . 10) Below is a table of values of two functions … http://www.owlnet.rice.edu/~ejl4791/practice test 1 solutions.pdf
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Math 200 Review: April 8, 2008 1. Find the derivative: (a) y …

Find the derivative: (a) y = (√ x +. 1. 3. √ x. )2. Solution: y = 2 … A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top) … http://www.dms.uaf.edu/~bueler/M200_KasiMID2rev_S08.pdf
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Math 201-103-RE – Calculus I Application of the derivative (2 …

Let x be the shorter side and y be the other side in meter. Total cost of the fence: C = 2x(100) + …. 10 x + 2 where x is the demanded quantity. Find: … http://jacusers.johnabbott.qc.ca/~gennaro.rispoli/c1ns/c1_derap2.pdf
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MA 121: Practice Final Name: Problem #1: Find the derivatives of …

Show that the derivative of f(x) = arcsin(x) is f (x)=1/. √. 1 − x2. Problem #10: Find the equation of the line tangent to the graph of xy2 = x2 − y … http://www.colby.edu/personal/s/sataylor/teaching/F08/MA121/PracticeFinal.pdf
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Math 249 Lecture 19: The Derivative Function Objective: To …

Find also the domain of the derivative. Answers: 1. (a) y = 15×2 + 24x − 3. (b) f (x) = 10×3/2 − 9. 4 x−1/4 − 28x−7/3 − 10. 7 x−9/7. (c) g (x) = … http://math.ucalgary.ca/~jling/2007/Fall/math249/Lectures/Lec19DerivativeFunction.pdf
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Chapter 4. The Derivative in Applications Lecture 3. Applied …

(cm3) occurs when we cut out squares whose sides have length 10 … Example 6(P.295) Find a point on the curve y = x2 that is closest to the point (18, 0). … http://math.bnu.edu.cn/~wangky/teaching/teaching4/03ZhuhaiCalculus/Chapter4/lec3.pdf
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Fall 2002 Derivative of ex and ln(x) Find the derivatives of the …

6. y = 20 (1 − e−x),. 7. y = x2 − 2 ln(x),. 8. y = 4 ln(x), … Take the difference of the populations in 1850 and 1860 and divide by 10 to estimate … Compute the derivative E (x). b. Find the energy expenditure when x = 10000, … http://www-rohan.sdsu.edu/~jmahaffy/courses/s00/math121/hwprobs/derivofe_ln/dexplnhw.pdf
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About Derivatives II_Examplesx

2 f ‘(x) = 10x. 3. + 9x. 2. + 10. (5x + 3). 2. Chain Rule. • Find the derivative of y = (x. 2. – 3x + 10). 4 f(x) = x. 2. – 3x + 10 n = 4 f ‘(x) = 2x – 3 … http://atrium.lib.uoguelph.ca:8080/xmlui/bitstream/handle/10214/1964/About Derivatives II_Examplesx.pdf?sequence=3
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7.4. Derivatives of Logarithmic Functions 1. Find the derivative …

−4 + 10x. 9 − 4x + 5×2. ) 4. Find the derivative of the function log2(1 + 8x − x2). solution: By the base change formula, … x2 = 2x. (b) The derivative of y is solution: y = y · 2x = ex2. · 2x. 6. Evaluate. ∫. −75. 2 x2 − 75 … http://www.math.okstate.edu/~seonkwon//7p4spr2006.pdf
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Rules For Finding Derivatives

EXAMPLE 3.7 Find the derivative of √625 − x2/√x in two ways: using the quotient … numerator, like 10/x2. Of course you can use the quotient rule, … The curve y = 1/(1 + x2) is an example of a class of curves each of which is … http://www.whitman.edu/mathematics/multivariable/calculus_03_Rules_For_Finding_Derivatives.pdf
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Name: REVIEW B – Derivatives Chapter 1. Differentiate y = sec 2 …

Find the second derivative of the function y = 7×2 + cos 2x. 19. Find dy dx . x2 + 3xy + y3 = 10. 20. Find dy dx . √ xy = x − 4y. 21. Find dy … http://www.mathman16.com/assignmentpages/DerivativesTest2review.pdf
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Geometrical Applications of the Derivative

Geometrical Applications of the Derivative Review. 1. Find the equations of the tangent and the normal to the parabola y = x2 – 2x + 1 at the point ( … http://www.rism.ac.th/class/hs/joem/review/Geo Applic of the Deriv .pdf
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Solutions to Test 2 1. Use the definition of derivative to find f …

Find the derivative and simplify: f(x)=(x2 + 1)6(3x + 5)4. … 4x2since y = √16 − 4×2. 10. Find dy dx by implicit differentiation: x2 + 4xy + y3 = 16. … http://homepages.ius.edu/WCLANG/m215/2009_fall/test2sol.pdf
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Section 2.7 Derivatives of powers of functions

g(x) = x2(x3 + 2x)10? (b) Find the derivative of the function from part (a). Do not simplify the answer. Solution. (a) The polynomial y = x3 + 2x is … http://math.ucsd.edu/~ashenk/Section2_7.pdf
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Calculus Derivatives of inverse functions and some review 10/22/09 …

It is possible to find the derivative of f 1(x) at x = 2. … inverse of y at x = 2Ï€/3. Some review of logs and exponential equations. … http://lhs.lexingtonma.org/Teachers/Williams/LHS Website jim_files/calc assignments/der of inv and rev.pdf
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MATH 1210 – Exam 2 Solutions – Fall 2009 1. Find the derivative of …

4. Find the second derivative of the function g(x) = x + 1 x − 1 … Assume we have a relationship between x and y given by x2 + y3 − xy = 8 …. 10. (a) True or false: If a function f(x) is increasing on (−∞, 0) and decreasing on … http://people.virginia.edu/~svd5d/files/093-1210/test-2-solutions.pdf
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MATH 229 Review Sheet for Exam 2 1. Section 10.6 The Derivative (a …

x3 − 3×2 + 8x − 10; m = 0 v. Just find the values of x where, f(x) = x3 … x2 ; m = 1/4. (d) Find dy du. , du dx and dy dx . i. y = u3 and u = 2×2 + 3x … http://www.mnstate.edu/goytadam/teaching/MATH229FS07/Exam2_Review.pdf
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Worksheet 2 – Derivatives Solutions September 28, 2009

(a) The derivative of an even function is an odd function. …. y = 1. 2. (x − 1), y = 1. 2. (x +3)+2. 10. If f(x) = x2/(1 + x), find f (1). Solution. … http://math.berkeley.edu/~preskill/math1a/worksheet2soln.pdf
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SOLUTIONS TO EXERCISES by Pit-Mann Wong HW 28. Find the …

h. y = x2 cos x y = (x2) cos x + x2(cos x) = 2x cos x − x2 sin x. … 10. (tan x) = sec2 x. 11. (cot x) = −csc2x. 12. (sec x) = sec x tan x …. (a) Given that 1 − xy = x − y. Find dy/dx and the equation of the tangent at the … http://www.nd.edu/~pmwong/SolutionsToHW.pdf
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Differentiation worksheet #2 for Calculus 1 Say f and g are …

x2. In the following problems, u is a function of x. For each given function, find the derivative with respect to x, in terms of u and du/dx. Example. For y … http://www.math.tamu.edu/~zteitler/teaching/derivativeworksheet-2.pdf
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Exam 4 Review Worksheet 1. Use logarithmic differentiation to find …

e(x2). 3. Find the area of the bounded region between the graphs of y = |x| … 10. Let f(x) = x2 − 1 and let P be the partition of the interval [−3,2] … http://www.math.umd.edu/~greggo/140/exam4review.pdf
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Concavity and the Second Derivative Test

10-9-2005. Concavity and the Second Derivative Test. If y = f(x) is a function, … Find the second derivatives of the following functions. (a) y = x2. … http://marauder.millersville.edu/~bikenaga/calculus/conc/conc.pdf
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Math 147: Review Sheet for Third Test 2.7 Implicit Differentiation …

(0, 0), (2 3√2, 2 3√4). D. (2) Find y if sin(x + y) = y2 cos x. … (4) A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder …. So x = 1 and x = 3 are local minima, since the derivative starts negative … http://www.math.utk.edu/~jconant/review147answers.pdf

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