use definition to show that the function f(x)= |x|^3 is differentiable at 0, with derivative equal to 0.

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: Let f(x) = x2 – 2.x. Use the definition of the derivative to calculate f'(3) %3D -

A:

Q: use the definition of derivative to find f prime (x). f(x)= 3(2x-1)^3

A: Given function is fx=32x-13. To find the derivative of the function using definition of derivative.…

Q: F(X) = X + よ2 %3D

A: Given, fx=x+3x2

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

A:

Q: Find the derivative of the function. f(x) = (9x2 – x) In(x) f'(x) =

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: se the definition of a derivative to find f '(x) and f"(x). f(x) = 3x² + 6x + 3

A: Given,           fx=3x2+6x+3

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

A:

Q: Use the definition to compute the derivative of the function f (x) = Vx2 + 1.

A: We have to find derivative

Q: Find the derivative of the function. 8x f(x) = In f (x) =

A:

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

A:

Q: Let f(x) = 4x² +. Use the definition of the derivative to find f'(1) %3D

A: To find- f'(1)

Q: Use the definition of derivative to a) f(x) = x - 2r? b) f(- %3D

A:

Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

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: 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: Use definition to find the derivative of the function f (x) = 5x- 2x at = 3. [2 Marks] %3D

A:

Q: Find the derivative of the function. f(x) = (x2 + 3) In(x) f'(x)

A:

Q: Use the definition of differentiation to find the derivative of the function f(x) = 4 - Vx +3. Is…

A: Given: The given function is f(x)=4-x+3. The objective is to find the whether the derivative of the…

Q: 3 Use the definition of derivative to find f'(x) for f(x): II

A: Given:

Q: 6. %3D F(x) = 5x

A: f(x)=65x

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: Use the Quotient Rule to find the derivative of the function. x2 h(x) = %3D X + 2 h'(x) =

A:

Q: Use the first principles definition of the derivative to find f'(x) where f(x) = √x

A:

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

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: Let f(x) = 4x² +. Use the definition of the derivative to find f'(1). %3D

A: To find the derivative of f(x) at x=1 using the derivative definition.

Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

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

A:

Q: Let f(x) = 4x² + . Use the definition of the derivative to find f'(1). %3D

A: We can make it easier for you

Q: Use the definition of derivative to find = f'(x). f(x) = for 1 3x

A: Given f(x)=13xf'(x)=limh→0f(x+h)-f(x)h=limh→0(13(x+h))-13xh=limh→013x+3h-13xh

Q: Help to find the derivative of f(x)=1/3x.

A: The given function is fx=13x

Q: Use the definition of the derivative to find the derivative of f(x)=8x+0 f^1 (x)=

A:

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

A: We have to find the derivative of the given function.

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: Find the derivative of the function. f(x) = (x² + 8) In(x) f'(x) =

A: In this question we need to find a derivative of the given function

Q: Use the first principles definition of the derivative to find f'(x) where f(x)=3x2 - x

A: This question can be solved by applying the concept of limit which is used to define the first…

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

A:

Q: 9. Use the definition of a derivative change of the functions below at f(x)% = x² + 2x

A:

Q: Help to find the derivative of f(x)=1/4x. ?

A: given f(x)=14xwe have to find the derivative of given f(x)

Q: Explain how to find the derivative of the function f(x) = cxn .

A: we have to explain how to find the derivative of the given function f(x)=cxn

Q: What is the derivative of f(x) = 1 over x⁵

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

Q: F(x) = Vx +3x %3D

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: Use the definition of derivative to find f (x) if f(x) = Vx+3.

A: fx=x+3

Q: Use the first derivative test to determine the relative extreme values of the function. below. a.…

A: local minima or relative minima is a point on the x-axis at which function has the lowest output…

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: Use the definition of the derivative of a function to determine f'(x) where f(x)=-

A:

Q: Use the definition of a derivative to find f'(x) for f(x) = v2x

A: Solution:Given     f(x)=2xTo find f'(x)Formula:By the defition of derivativef'(x)=limh→0f(x+h)-f(x)h

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: