Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative. Enter the derivative of F(x) using prime notation, i.e., as F'(x). (F(x*)) =

Q: If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.

A: Given,

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. f(x) = (9x2 – x) In(x) f'(x) =

A:

Q: If f(x)=4/x, find the derivative of f(x) at x=2 using the limit definition of the derivative at a…

A: given function f(x)=4/x we have to find a) the the derivative of f(x) at x=2 using the limit…

Q: 2 f(x) = ; 2x-1

A:

Q: Find the derivative of f(x) = In(x² + 1) %3D

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: Calculate the derivative of f(x)=4x³ with respect to x and evaluate this derivative at x=2.

A:

Q: Let f(x) = x^2 - 4x + 1. What is the equation of the tangent line to f(x) at x = 2? Use the limit…

A: Please see the below picture for detailed solution.

Q: Find the derivative of: f(x) = (x3 + 2) In(x)

A: Consider the function

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 f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: Calculate the derivative of the function below using the quotient rule. 2x ม 5x + 3 f(x) = and g(x)=…

A: Quotient Rule : If  y = f(x)g(x)  then  y' = g(x)·f'(x)-f(x)·g'(x)g(x)2.

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: Use the definition of a derivative to determine all points for the function f(x) = ((x+|x|)^2)+1 is…

A:

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

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: By using the limit definition of a derivative, determine the derivative of f(x) = 1/x at x  = 2

A: By using the limit definition of a derivative, determine the derivative of f as shown below:…

Q: Suppose that the second derivative of the function y=f(x) is y'' = (x-3)(x+9). For what x-values…

A:

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: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

Q: 3) Find the derivative f(x) = xe-*In(x³) %3D

A:

Q: Find the derivative of the function. (x) - In(4 - x") f'(x) -

A: Find the derivative of the function.      fx=ln4-x8

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: f(x) = x In x

A:

Q: Use the formal definition to find the derivative of f(x) = 4 at x = 8. x+3

A: To find the derivative of the function  f(x)=4x+3 at x=8

Q: Where does the derivative of g(x)=(x^2)/((x^2)+3) = 0 or is undefined?

A: Given function, gx=x2x2+3

Q: Use the limit DEFINITION OF A DERIVATIVE to find the derivative of the function. 16) f(x) = Vx + 5…

A: The derivative of a function y=f(x) is given by f'x=limh→0fx+h-fxh. The given function is fx=x+5.

Q: Let f(x)=9−(4x^2+3x). Then according to the definition of derivative

A:

Q: 1. Evaluate the derivative of f (x)= sec(In(x²)). DO NOT SIMPLIFY.

A:

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

A: Considering f(x) = 9 – 5x. To find the approximate derivative of f(x) at x = 2.

Q: Find the derivative of the following with respect to x: 1. f(x)=4log3x-In x

A:

Q: Find the derivative of the function. g(x) = 9 + In(x)

A: We have to find the derivative of : g(x)=ex29+ln(x)

Q: Find the derivative and state the domain of f(x) = In(x + 4) %3D

A: In this question, concept of derivative is used. Derivative The derivative expresses the rate of…

Q: o f(x) = 4~/x+3

A: by using definition of a derivative.

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: Find the derivative of the function. f(x) = 4x In 4x f'(x)=

A:

Q: Given f(x) = ||+x, at which point does the derivative not exist? Mathematically show that the…

A: According to question given that f(x)=|x|+x"A function f is said to be differentiable at a if  f'(a)…

Q: What is the limit that will calculate the derivative f'(2) for the function f(x)= x-1

A: solution of the given problem is below...

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

A:

Q: Give three different notations for the derivative of ƒ with respectto x

A: Definition used -     Derivative of a function -       It is the rate at which the y value of…

Q: Find the derivative of f(x)=x^1/2 at x=1/144

A:

Q: Find the derivative of f (x) = 5² In (x).

A:

Q: Find the derivative of the following function by definition (from first principle): 1-x f(x) =. 2x

A:

Q: find the derivative of f(x)=x/(x+2) using the limit definition of a derivative

A:

Q: Find the derivative of the function.

A:

Q: Find the derivative of f(x)= 11x^2 at x=1

A: Given:    f(x) = 11 x2  at x = 1

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 f(x) = 1 over x⁵

A: here we use the formula of derivative  ddxxn=nxn-1

Q: Find the derivative of the following function by definition (from first principle): f(X)=1-x/2x

A: