Let f(x) : 1 + 3x – 4 and let h be the inverse function of f. Notice that f(-2) = –14. h'(-14) =

Q: Show that is C is a function of x with derivative C'=C/x and N=C/x, the d/dx (C/x)=(C'-B)/x

A:

Q: Give the derivative formula for the function. j(x) 4 In x e5 = j(x)

A: The function is given by,

Q: Find the derivative of the following function F(x) = (21 – 1)° dt %3D using the Fundamental Theorem…

A:

Q: Consider y = f(x)=√1+2x, x 2-1/2. Without finding x = f(y) explicitly, find the derivative of the…

A:

Q: Consider the function, f(x) = (x + 1)ln(5x² + e). Without finding explicitly the inverse of f(x),…

A: Given : fx = x+1ln5x2+e

Q: Find the derivative of the following function F(x) = (2t – 1)³ dt using the Fundamental Theorem of…

A: Here I am attaching image so that you understand each and every steps.

Q: Find the derivative of the inverse function s(x) if f(x) = -x+ 1 1 r + 1

A:

Q: (3) Let y = f(x) = x2 +1, evaluate the derivative of the inverse function x = f-(y) at y = 2. %3D

A: Given :           y=fx=x2+1

Q: write the function as a composite f (g(x)) and compute the derivative using the Chain Rule. y = (x +…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Compute the derivative of the following function. 1(x) = 3e 3x f'X)%3D

A: Topic - differentiation

Q: 18. If f (x) = es*, find (f-1)'(1) using Theorem 7 (Derivative of the Inverse Theorem).

A: We have to find derivative

Q: 2. g'(x) where g(x)= x² +7x-5 %3D

A: ddxxn = n·xn - 1, and ddxC =0

Q: Let y = (x + sin(x))³. Find g(æ) and f(x) so that y = (f o g)(x), and compute the derivative using…

A:

Q: Find the derivative of the function. r(x) = In(x + 1) + 5x7ex r'(x) =

A:

Q: Let y = f(x) = x² +1, evaluate the derivative of the inverse function x = f-l(y) at y = 2.

A: Given a function, y=f(x)=x2+1 To find the derivative of the inverse function of f(x).

Q: Compute the derivative of the given function. f(x)=−4x^π+4.1x^1.3+π^1.3

A:

Q: write the function as a composite f (g(x)) and compute the derivative using the Chain Rule. y =…

A: Given : The function is y = cos ( x3 ) .

Q: Obtain the first and second derivative of the following real-valued functions 1. ƒ : R → R, such…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 2. g'(x) where g(x)=x² +7x-5 %3D

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

Q: use the Power Rule to compute the derivative.

A:

Q: Find the derivative of the inverse of f(x)= x° +1 using the formula dy 1 off "(x)= g'(x) =- f'(g(x))…

A: Topic:- application of derivatives

Q: The derivative of f(x) = 2 cos 2x is an odd function.

A: Odd function

Q: Find the derivative of the inverse of f for t = 0,

A: The derivative of a definite integral is given by the second fundamental theorem of calculus as…

Q: A. Compute the derivatives of the following functions 1. f(x) = xe3x-sinx %3D

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: f. y=In(x8+1)

A: We will solve the problem

Q: · f(x) = sin(In r²) %3D

A:

Q: For x > 0, find f'(x) where f(x) = x*¯+3) via logarithmic differentiation. Show all ur work.

A: Topic:- application of derivatives

Q: if f(x) = x²√√In x² P x A. f'(x) = . find the derivative of this function f'(x) 1-In x² x²√√In x²…

A:

Q: 3 Find the derivative of the inverse of f(x) = x +1 using the formula dy %3D 1 off "(x)= g'(x)= dx…

A:

Q: Find the second derivative of the function (r² + 1)(x² _ z +1) U =

A:

Q: Find the derivative of the following function x4 F(x) = (2t – 1)3 dt using the Fundamental Theorem…

A: Consider the given function in the form of the definite integral for f(t).

Q: Find the derivative of the function ffor n = 1, 2, 3, and 4. sin x fx) = - (X), I n =4 Use the…

A: Solve for the derivative

Q: Find the derivative of the following function F(x) = (2t – 1)3 dt using the Fundamental Theorem of…

A: SOLUTION-

Q: Let f(x) = 8x +x – 7. Find the derivative of f by using the formula %3D and check your result by…

A:

Q: Let y = (x + sin(x))³. Find g(æ) and f(x) so that y = (f o g)(x), and compute the derivative using…

A:

Q: Find the derivative of each function e 2x a. f(x) = 2x+1 b. f(x) = In Vx + 2x %3D c. f(x)= x?e* – 6x…

A:

Q: Find the derivative of the following function (2t – 1)* dt F(x) = using the Fundamental Theorem of…

A:

Q: Let y=(x+sin(x))^5 Find g(x) and f(x) so that y=(f∘g)(x), and compute the derivative using the…

A:

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=4f(0)=4 and…

A:

Q: Find the derivative of the function. u(x) = (x2 + 1)9x2 − 1 u'(x) =

A: The function u(x) is:

Q: Let y = f (x) = x² + 1, evaluate the derivative of the inverse function x = f-1(y) at y = 2 %3D %3D

A: y=fx=x2+1.

Q: 3) Use the definition to find the derivative of f(t) = +1 t+1 %3D

A: f'(t) = -1/t2

Q: Use the u-substitution to find the anti-derivative of h'(x)= xcos(2-3x2)

A: h'(x)=xcos(2-3x2) Formula ∫cos (x) dx= sin (x)+C

Q: Find the function whose derivative is Inx+1. A) xlnx B) x+xlnx x+1/x D) x+Inx

A:

Q: Let f(x,y) x2-2y² +3x. In what direction from (1,2) should we proceed so that the change in f in…

A: A function f(x,y) from a point increases most rapidly in the direction of its gradient at that…

Q: Use implicit differentiation to prove that d/dx [ xn ] = nxn − 1

A: Here we use implict differentiating to prove thatddxxn = nxn-1

Q: Find the linearizationsof the following functions at x = 0. tan x

A: Linearization is tangent line at a point x=atangent equationy-y0=mx-x0m=f'a

Q: (2x2 -r+1) In(x)+2(cos(z² +3)| f(x) =

A: Quotient rule of differentiation:…