Question 2. Given that f'(x) = 4.x(x² + 8)-1/3 and f(0) = 0, find the function f(x).

Q: Question 2 If f(x) = S dt for x > 1, find f'(2). 1+lnt

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Q: ) = 5 + 4 sin(x). If f(0) = 3 and f' (0) = 4, what is f(x)? Consider the function f(x) whose second…

A: Given:

Q: 3. Find the first and second derivatives of the function f (x) = e¬²

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Q: Question 8 of 25 > Find the derivative of the function f. 3 √x f(x) = O At

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Q: Question 2 Consider a function f with domain {x|x # 0} and the following derivatives: f'(x) = bx=1…

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Q: Question 15 Find the derivative of y = 32x+5 A. 2 ln 3 (3²x+5) B. In 3 (3²x+5) C. 2ln 3 D. 32x+5 O B…

A: Given function is y=32x+5. To find: Derivative of the given function y=32x+5. Formula used: 1)…

Q: Q3: i) Find the derivative of the function of y = (x² + 1)sin 3x %3D (ii) Find the absolute maximum…

A: Given:  i) y = x2 + 1sin3x ii) f(x) = x2-13, -3≤x≤3

Q: Question 5 Determine the derivative of the given function: y = 5-2 Oy = 5"-2 (In 5)(x - 2) Oy = 5-2…

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Q: Question 9 Find the derivative of (3x+4)3 (-3x 2)4 h(x) = You should leave your answer in factored…

A: Given function isThe given function is a rational expression and the derivative can be obtained…

Q: Question 7 [6;4] (a) Find the derivative of the function y = 2x² + 12 when x = 2.

A: Answer

Q: Question 21 Given the function f(x) = x to the 3rd power -6x + 2, find the value of the first of the…

A: Differentiate wrt x

Q: Question 9 Suppose 8 (x) = sec-(x²), what is the derivative of g with respect to x? 2x A 8 (x) =…

A: We need to find derivative.

Q: Question 20 Given the function fx) x to the 3" power 6x 2. find the walue of the first of the first…

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Q: Question 9 Suppose 8 (x) = sec-(x2). what is the derivative of g with respect to x? 2 A 8 (x) = x4-1…

A: We have to choose the correct answer from the given options according to the given information

Q: Question 2. Find the derivative of the given functions: a) y = e5 log, (4x® + e2=) In(x² + 4)ez b) y…

A: We know that u·v' = u·v' + v·u' uv' = v·u'-u·v'v2

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cos

A: Topic = Derivative

Q: Question 31 Compute the derivative function f' (x) algebraically. f (x) = -5x³ + 7 O f' (x) = –15x²…

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Q: Question 11 What is the derivative of y =V x3 -2x² +x -2,

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Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: given: f=x3y2-yx+lnx to find:fyyxxx

Q: Question 6 You do not need to simplify the answer. :) For each of the following, use the quotient…

A: Given,  f(x)= (x2+x)x-2 = (x2+x)/x2 = (1+1/x) differentiate with respect to X, f'(x)= d/dx 1 + d/dx…

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given :             cosh(3x2y) = x + ln(exy + 1)   To find :            ∂y∂x

Q: Question (3) Estimate the first and second derivatives of f(x) =-0.1x 4 - 0.15x 3 - 0.5x 2-0.25x+…

A: Solution:Estimate the firts and second derivative of fx=-0.1x4-0.15x3-0.5x2-0.25x+1.2at x=0.5  and…

Q: Find the equation of the line tangent to the graph of f(x) = (In x)? at x= 8.

A: f(x)= (lnx)2

Q: What is the relationship between the functions In r and e?

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Q: On what interval is the function f(x)=x^2e^x concave downward?

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Q: Question 4 Given f(x) = x² – x 1) Derive the derivative function f'(x) using the limit definition of…

A: Solution is given below

Q: QUESTION 3 Given that f (x) = 2x2 + 1. Find f'(x) using the definition of derivative. %3D

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Q: 1. Find the derivative of the following functions. (find y') a. у %3DIn(cos(20)) b. cos(xy) = x - y…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: -1 The derivative of the function y = sin Va at 1 is equal to 4

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Q: Question 2 Let a be a real valued constant. Find the derivative with respect to x: Y = 4ae 1-4ae4z O…

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Q: Suppose f(-3) = 3, f'(-3) = 5, = -8, and %3D g(-3) = 1, gʻ (-3) = H(x) = f(x)e®(x). Find the…

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Q: 5. Given b(x) = (3x – 7)*, if m(x) = 36 (2 tan-1 (1 – 7x)) then m' (x) is %3D %3D

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Q: Question 1 Find a classify the critical points of f(x)=-, using the two methods we learned in class:…

A: The given function is :f(x)=x55-x33 To find: Critical points of f, and  we need to classify them…

Q: Question 1 Apply the First Derivative Test to find the minimum value of f(x)=(2x^+2)/x² . Keep 4…

A: The given problem is to find the minimum value of the given function using the first derivative…

Q: Question 13. Obtain the derivative of the function f(x) = 2 ln(4x) Enter the answer as a function of…

A: topic - derivative

Q: Find exact value(s) for x such that 3e" - e' = 0.

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Q: x2 + 1 Find a formula for the tangent line for y = at x = 1. x + 1 e rational function does not…

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Q: Example3: a) Find the derivative of f(x.r.:)= r - -: : at P(1.1.0) in the direction of 1= 2i-3j-6k.

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Q: Question 3 Find the derivative of each of the following functions. f (x) = x + 9 а. b. f (x) = In(x²…

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Q: 1. Find the derivative of f(x) = e" (x² – 1)ª. Make any obvious simplifications.

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Q: Question 36 Evaluate the first derivative of the implicit function 4x- +2xy +y OA (4x-y)/ (x + y)…

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Q: Can you help me step by step?

A: Given function is

Q: 2. Find the first derivative of the following expression: f(x) = (x2 + 1)sin a

A: take derivative  use the exponent rule

Q: Question 1 Find the derivative of f(x) = 2x +3 Provide your answer below: f'(x) =O

A: Answer and explanation is given below

Q: Question 3 Algebraically compute f'(1) using the definition of the derivative, given that f (x) = x2…

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Q: Question 13 4 Find the derivative of y= 3/x x3 A 1 y'=3 4 y'=3 x4 1 B 6. C y' x1 12 3x2 x2 3/2 12 D…

A: Please see the answer of question 13 below. According to the guidelines of Bartleby, only the first…

Q: Question 1 a) Using the method of first principle find the derivative of the function 1 f (x) =

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Q: Question 12 VI² – 1 What is the derivative of y O y = 1 1 - 1 O y' %3| 22-1 O y' =

A: Given query is to find the derivative of the expression.

Q: Question 21 Evaluate the first derivative of the implicit function: 4x2 + 2xy + y² = 0 4x +y (A x +y…

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Q: In finding the root with Newton's Method, an initial guess Xo = 4 with f(Xo)= 1 leads to X1 = 3.…

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