Assuming g is a differentiable function, find an expression for the derivative of f(x)=(x^2) (g(x)).

Q: What is the derivative of x^6

A: We have to use exponent rule.d/dx(x^n)=n*x^(n-1)

Q: Choose the rule that you would use to most efficiently find the derivative of the function. f(x) =…

A: Given f(x) = 8√x^3

Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

A: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

Q: Find an equation of the tangent line to the graph of y = f ( x ) at the point on the graph where x…

A:

Q: How to use a graph of a derivative to determine the parent function.

A:

Q: show that nth derivative of  f(x)=x^2/(2x+1)(2x+3)

A: nth derivative of f(x)=x2(2x+1)(2x+3) f(x) can be written as by using synthetic division method…

Q: 2 - x f(x) = 3 x + 1

A: given that f(x)=2-x3x+1we need to find the derivative of the functionuse the quotient rule that is…

Q: Find the derivative of f(x) = 10/x

A: We can find the derivative as below

Q: Suppose that the function y in the Derivative Product Rule has a constant value c. What does the…

A: Derivative product rule:The derivative product rule for the functions x and y is given by,

Q: Explain what happens when the derivative of a differentiable function is zero ?

A: To explain when a derivative of differentiable function is zero.

Q: Find the derivative of [(xt1)*] /x.

A:

Q: find the derivative by using the definition of a derivativef(x)= the square root of x+1

A: We need to find the derivative using the first principles (without appealing to any standard…

Q: Find the derivative of f(x)=x tan x- cSc x.

A:

Q: find the derivative of the function F(x)=4(x^3-x)^4

A: According to the given information, it is required to find the derivative of the given function.

Q: Find the derivative of f(x) = - 2 * root(4, x ^ 5) + 7/(x ^ 6)

A:

Q: Use the First Derivative Test to find the relative extrema of x – 3 f(x) ex

A: The given function is fx=x-3ex. We need to find the realtive extrema. Concept used:  Consider x=c is…

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: Determine the derivative of h(x) = 15 arctan

A:

Q: Find the derivative of the function using the definition of derivative. f(x) = x4 f'(x) = %3D

A: To find the derivative of the given function using the definition of derivative.

Q: Find the relative extrema of the function f(x)= x2+3x+4 using first derivative test.

A: fx=x2+3x+4 To find extrema of function.

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: Find the derivative of the function g(x)=x3∫x2tdt.

A:

Q: calculate the 21st derivative of function f(x) = 20-x

A:

Q: Find the derivative of f (x) = -4 tan (x).

A:

Q: Use definition of derivative to find derivative of the function f(x)=3/x+2, at x=-1

A: Given f(x)=3x+2    at x=-1To find f'(x) at x=-1

Q: If f(x) = x³ + find f"(-1).

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find the function ƒ(x) whose derivative is sin x and whose graph passes through the point (0, 2).

A:

Q: Use the Product Rule or the Quotient Rule to find the derivative of the function y = −x2tan x

A: Use the Product Rule or the Quotient Rule to find the derivative of the function y=-x2tan x

Q: What is the rule for calculating the derivative of a composite of two differentiable functions? How…

A: Let us we consider a function which is real valued function which is composite of of two functions…

Q: f(x) = x' tan (5x)

A: Explanation and solutions is given below....

Q: Find the Do not include "f'(x) =" in your answer. derivative of f(x) = (-x³ - 2x² - 2x) sin (x).

A: Given f(x)=(-x3-2x2-2x)sin(x)

Q: Find 3rd derivative if ƒ'(x) = x³.

A:

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: 5+x f(x) = 3—х

A: Solve the following

Q: find the derivative that function  f(x)=xsinx

A: Given,          fx=xsinx

Q: Find the indicated derivative. f'(-5) = If f(x) = x², find f'(-5). X

A:

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

A: Given :   y = 11x2    at x =1

Q: h (x)= 3

A:

Q: Find the derivative of f(x) = 3/x at x = 3 by using the definition of derivative. Note that you will…

A: Given,f(x) = 3x at x = 3

Q: function

A:

Q: Find the derivative of f(x)=5-x/2sin2x

A: Consider the given function.

Q: Find the derivative of the function f(x) = 6x2 - 6 cosx

A: the given function f(x)=6x2-6 cos x

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: State the notation/symbol for: derivative of y with respect to x derivative of f(x) second…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the derivative of the given function by using definition of derivative  f(x)= sec(x)

A:

Q: How do you find the derivative of the quotient of two functions that are differentiable at a point?

A:

Q: Solve the derivative of f(x)=−1/√5 x.

A: we have to find the derivative. f(x)=-15x

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: