For the two functions g ( x ) = f ( 3 x ) describe the relationship between g ′ and f ′.

Q: For the following exercise, use the definition of a derivative to find f'(x) f(x)=x+(1/x)

A: The definition of derivative is  f'(x)=limh→0f(x+h)-f(x)h

Q: Find the derivative of the function. f(x) = 4e* – x2 f'(x) =

A: Simply use the power law of derivative and also derivative of exponential .

Q: Using the definition of derivative, find functions: a) y = xVx -2 .2 (b) y =- (x-1)

A: Given ,f(x)=xx2-2Therefore,f(x+h)=(x+h)(x+h)2-2We know that…

Q: use the graph of y=f(x)y=f(x) to sketch the graph of its derivative f′(x).

A:

Q: Find the derivative of the function. f(x) = V 5x + 4

A: Question number 1,Given,          fx=5x+4

Q: What is the derivative of f(x) = x² +x² a +2 where a is a constant ? xa+2

A: We write f(x) using exponents f(x)=x7+x2+a+2xa+2f(x)=x7+x2+(a+2)x-(a+2)

Q: Find f'(x) using derivative rules, f() = V + 2. メジ %3D

A: Given:…

Q: For the function f(x.y) = e 4xy, find f, and f,. f, =

A:

Q: For the pair of functions, find the derivative of the composite function f(t(x)) in terms of one…

A: The given pair of functions  ft=4t and tx=x2+7x To find the derivative of the composite function ftx…

Q: For the function f(X) = ax3 +ba2 +cx, find the second derivative, f"(X). Here a,b and c are…

A: Given Function,F(x) = ax3 + ba2 + cx

Q: For the pair of functions, find the derivative of the composite function c(x(t)) in terms of one…

A:

Q: Find the first and second derivatives of the function. f(x) = (x2 + 6)5 f'(x) %3D f"(x)

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Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 11 e* +…

A:

Q: Find the derivative of the function. 29 r(x) = r(x) = %3!

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find the derivative of the function g(x)=(5x^2−3x+1)e^x g'(x)=___

A:

Q: Consider the function f(x) = (x² – 6)(a² – 6æ) Compute the derivative. f'(x) =

A: In this we are going to use product rule of derivative to find out the solution so I'm providing…

Q: For the pair of functions, find the derivative of the composite function f(t(x) in terms of one…

A: Given,

Q: The derivative of the function f (x) = (x-1 – 2)(3 – Vx) is,

A:

Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

A:

Q: For the following exercises, use the definition of a derivative to find f′(x). 55.  f(x)=2−3x

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Q: a) Find the derivative of g(x) = 3tanx – 4cotx. %3D b) What is the value of g 3.

A:

Q: For the pair of functions, find the derivative of the composite function  f(t(x))  in terms of one…

A: Given  f(t)=2t and t(x)=x2+6x Now dfdx=dfdt·dtdx

Q: For the pair of functions, find the derivative of the composite function f(t(x)) in terms of one…

A: Given that the composite function f(t(x)) in terms of one input variable. f(t) = 3t ; t(x)  =x3   To…

Q: Find the indicated derivative and simplify. 12 f'(x) for f(x) = x2 - 4 %3D f'(x) =D

A:

Q: The derivative of the function y = 7x² + 12 – is: - 15 a) y' = 14x + x2 15 %3D b) y' = 14x + %3D c)…

A:

Q: For the function f(x): X-6 find T (x), the third derivative of f, and f(4)(X), the fourth derivative…

A: Given that:f(x)=x-2x-6To find f'''(x) and f(4)x

Q: From now on consider the function f(x, y) = e$n(x) y.

A: direction of fastest increase is along the gradient vector  Given f(x,y)=esinx y

Q: For the function f(x) = 3x² + 2x + 1, evaluate and simplify: f(x+h)-f(x) h Find the value of the…

A:

Q: Find the second derivative f"(x) for f(r) = e(z+2)*.

A: Given: fx=ex+24 for finding second derivative of given function we first take log and find first…

Q: Differentiate the function with respect to the independent variable. f(x) = - 8x+ e + e f'(x) = D

A:

Q: Given f(x) = 3 x² – 2 vx , which of the following expressions will represent the first step when…

A: Given,          fx=3x2-2xWe know that,          The derivative of a function, fx using the…

Q: Use the chain rule to find the derivative of f(x) = 2(10r° + 9®)™ You do not need to expand out your…

A: Given: f(x)=210x8+9x615

Q: For the pair of functions, find the derivative of the composite function f(t(x)) in terms of one…

A: Derivative: f(t)=ett(x)=9x-4f(x)=e9x-4We know,ddx(ex)=ex

Q: Find the derivative of the function. f(x) = e!/(9x) f'(x) = %3D

A:

Q: For the pair of functions, find the derivative of the composite function c(x(t)) in terms of one…

A:

Q: For the pair of functions, find the derivative of the composite function  f(t(x))  in terms of one…

A: Please see the explanation below

Q: Find the third derivative f"" for the function f(x) = I-5

A: The first derivative of is given as: Also the derivative of a function in form of is: The given…

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 12 e* +…

A:

Q: Given the function f(x, y) = x - y' + 2xy. Determine the derivative a?f/ əx² .

A: Find your answer below

Q: For the pair of functions, find the derivative of the composite function f(t(x)) in terms of one…

A: ft=t2+4,  tx=ex Now, ftx=fex=ex2+4=e2x+4

Q: Find the derivative of the function g(x)=(5x^2+2x−1)e^x g'(x)=____

A:

Q: For the pair of functions, find the derivative of the composite function c(x(t)) in terms of one…

A:

Q: For the pair of functions, find the derivative of the composite function f(t(x) in terms of one…

A: Given:f(t)=5lm(t),t(x)=5x3-4x2+9x

Q: For the following exercises, use the definition of a derivative to find f′(x). 57) f(x)=4x^2 61)…

A:

Q: For the function f(x,y)= x^2 +2y^2 Use the first derivative test to determine if the function is…

A: Given function

Q: Find the derivative f'(x) for the function f(x) = x² + x – 17. - O A. f'(x) = 2x – 16 В. f («) — 2а…

A: Find the derivative of f(x)

Q: For the pair of functions, find the derivative of the composite function f(t(x) in terms of one…

A: Given,

Q: For the pair of functions, find the derivative of the composite function f(t(x) in terms of one…

A: Given,