Use the following graph of f(x) to describe the behavior of f '(x). State where f '(x) is positive, negative, zero or not defined.

Q: f(x) = (x + 2)2/3 -

A: First we have to find f'(x) . And to find extrema by first derivative test we have to find all roots…

Q: Find the derivative of the function.

A: Given: To find: Derivative

Q: Find the derivative of the function f(x) = (In x)°.

A: Given that,             f(x) = lnx3 Differentiating with respect to x, we get                  f'(x)…

Q: Find the second derivative for the functions defined as follows.h(x) = x/ex

A: Given:             f(x)=xex

Q: Find the derivative of the function.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

Q: Find the second order derivative of f(x) exsinxcos2x

A:

Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

A:

Q: Define the derivative of f(x) at x

A: Consider a function f(x) The differentiability of a function:  Let f(x) be a real valued function…

Q: Consider the function f(x) whose second derivative is f”(x)=5x+2sin(x). If f(0)=4 and f’(0)=4, what…

A:

Q: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: Find the derivative of the function. f(x) = In(x + 1) f'(x) =

A: To find the derivative of the function fx=lnx+1

Q: Find the derivative of the function. f(x) = 4 3 VX + 2cos x

A: Here, the given function is: f(x)=4x3+2cos x

Q: Find the derivative of the function. h(x) = x2 arctan(5x)

A: Given function: hx=x2tan-15x Differentiate the above function w.r.t "X" h'x=ddxx2tan-15x

Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

Q: Find the derivative of f(x)=arctan(1/x) and simplify

A:

Q: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

A:

Q: Find the derivative of the function. f(x) = 2x In(x) f'(x) =

A: Let us consider the given function as: fx=2xlnx By using product Rule of derivative, we get:…

Q: What is the derivative of the function with respect to x of (x + 1)³ – æ° -

A: Given : Function x+13 - x3   To find : Derivative of the given function with respect to x?

Q: Find the derivative of the function. f(x): f(x) = 2xarccos(x) – 2/1 – x² 2arccos(x) + 2 2arc cos (x)…

A:

Q: Develop a general rule for the nth derivative of xf(x), where f is a differentiable function of x.

A: Given: the function xfx, where f is a differentiable function of x.

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=2 and f'(0)=3, what…

A:

Q: 3 f(x) :

A:

Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

A:

Q: Suppose that the second derivative of the function y = f(x) is y" = x*(x = 2)°(x + 3). For what…

A: Given: The second derivative of the function y=f(x) is y"=x2(x-2)3(x+3) Definition: The inflection…

Q: Find the derivative of the function. h(x) = x² arctan(8x) %3D

A: To find the derivative of hx=x2tan-18x

Q: Find the derivative of the function. • 2x2 g(x) = 1 dt 3 + t3 /tan x g'(x) =

A:

Q: Calculate the derivative of the function below using the quotient rule. x4 y = Vx + 2x4 f(x) = and…

A:

Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Let f (x) = 7 cos(Tx). Find the twentieth derivative of f (x).

A:

Q: Find the derivative of the function. f(x) = arctan(3x)

A: We  can make it easier for you.

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: Compute for the derivative of the function f(x)= Arctan (csc2 (3x2/3))

A: Some derivative formulas: ddxtan-1x=11+x2 ddxcscx=-cotx cscx Chain rule of derivative:…

Q: the first derivative of a continuous function y=f(x) is y'=x(x-12)^2 .find y'' and then use the…

A:

Q: Find the derivative of the function f(x) v4-x by definition

A:

Q: Use the General Power Rule to find the derivative of the function. g(x) = V7- Sx

A:

Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f'…

A: Use differentiation of trigonometric function

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

A:

Q: Compute the derivative of the function f (x) = tan x2 +1

A:

Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

A:

Q: Compute the derivative of f(x) = arcsin(x² e3=).

A:

Q: Find f (x) of f(x)= by using the definition of the x- derivative.

A: Definition of Derivative is given as

Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

A:

Q: Find the derivative of the function f(x) = v4-x2 by definition

A: The given function is f(x)=4-x2 The definition of the derivative is given by: If a function f(x) is…

Q: Find the derivative of the function. h(x) = x² arctan(8x)

A:

Q: Find the derivatives of the following function f(X) from the first principle xsinx

A: derivative of xsinx by first principl is xcosx+sinx. for this question see 2nd step.

Q: Use the definition of derivative to compute f '(0). e-1/x if x * 0 if x - 0 f(x) f '(0) -

A: The definition of the derivative is given by: f'(x)=limh→0f(x+h)-f(x)h⇒f'(0)=limh→0f(h)-f(0)h  ...…

Q: Consider the function f(x) whose second derivative is f''(x)=8x+8sin(x). If f(0)=4 and f'(0)=4, what…

A: