3. If G(x) = tan x, find G(t/6), G(x - x/2), G(-x) and express G(2x) as function of G(x).

Q: Use the definition of the derivative, f'(x) = lim z+h)-(2) to findf' (x) where f(x) = x³ +1. h→0 O…

A: fx=x3+1

Q: Suppose that the function ƒ(x) and its first derivative have the followingvalues at x = 0 and x =…

A:

Q: Determine the derivative of the following function: f(x) = 3ecos(3x) cos(3 x) O 9e cos(3 x) O…

A: f(x) =3ecos3x differentiating function with respect to x

Q: 1. Find the derivative of the following function: f(x) : (x² sin- if x ± 0 if x = 0

A:

Q: 2ƒ(x), x = 2

A:

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

Q: From the definition of the derivative of f(x) as f (x+h)- f(x) f (x)=lim h→0 h derive a formula for…

A:

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: Given that the function f(x) = | x - 1|

Q: Find all anti-derivatives for the following function. g(x) = -4 cos(x) – x

A: NOTE: Refresh your page if you can't see any equations. . take integration(anti-derivative)

Q: Find the derivative of the following: 1. y=x(V1- x³ ) 1+x 2. у-. 1-x (x³+5) V4-x² 3. у — x*-x2+6 sin…

A:

Q: Find the derivative of the following. 2. g(x) = sin x tan x 1+sin x 3. h(x) = 1-sin x x+4 4. i(x) =…

A: 2.g(x)=sinx tanx3.h(x)=1+sinx1-sinx4.i(x)=x+4cosx5.j(x)=[(x2+cosx)(2x-sinx)]

Q: Find derivatives of the functions defined as follows:

A: Given: fx=ex3x+2

Q: Find derivatives of the functions defined as follows: y =(3x3 - 4x)e-5x

A: Given:          y=3x3-4xe-5x Let:  y=f(x)=3x3-4xe-5x Product rule of differentiation is given by…

Q: b) Find the derivative f'(x) in the following cases. 5x+1 1. f(x) = 2x-1. 2. f(x) = 3. f(x) = csc x…

A:

Q: 2. g'(x) where g(x)= x² +7x-5 %3D

A: ddxxn = n·xn - 1, and ddxC =0

Q: Can you help with this problem step by step?

A: Given,

Q: Find the derivatives of the functions g(x) = tan 3x/(x + 7)4

A:

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: fx=cosxxn When n=1, fx=cosxx Differentiating with respect to x, we get…

Q: Let k(x) = tan−1 x. Find the value of k(9)(0), the 9th derivative of tan−1(x) at x = 0.

A: Given

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

A: Odd function

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A:

Q: 1. Let f(x) = Find the equation of the tangent line to the graph of f'(x) at the point x² + 1 where…

A:

Q: Suppose that a function f(x) has derivative f' (x) = g(x)+ h(x) for some functions g(x) and h(x).…

A:

Q: Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Find the derivatives of the following: 1.) x* + 2y = 6x 2.) f(x) = (tan 5x) (x + 2)²

A:

Q: (1) For every natural number n, x" = nx"-1 (you may use the product rule for derivatives and that x…

A:

Q: Use the chain rule to find the derivatives of f(x) and g(x) as well as f'(0) and g'(0): f(x) = (2x³…

A: According tp our guidelines we can solve only one question so we are solving 2nd question for you.…

Q: Consider the following. g(x) = 2e-x + In x; h(x) = 5x2.1 Find the derivative for f(x) = g(x) · h(x).…

A:

Q: For the function given by g (x) = x2 + 2x +1, use the limit definition of the derivative to compute…

A: Please refer the attached image for complete solution.

Q: Which of the following function has 10" derivative equal to zero? A f(x) =(3x²-4x +2)³ B f(x)…

A: Here we find out whic function 10th derivatives is zero.

Q: If f(x) = sinx and g(x) = cosx, then what is the relation between g'(x) and f""(x)?

A:

Q: Find the second order derivatives of the following functions f(x) 3x - x' i) Tan 1-3x

A:

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: 1 Let f(x)=- (3x – 5)² -6 and f'(x) = %3D (3x – 5) Find an equation of the line tangent to the graph…

A: The given function is: f(x)=1(3x-5)2

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. f(x) = x² sin x n = 1 n = 2 n = 3 n =…

A:

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: Given:fx=cos xxn for n=1,2,3,4Formula:ddxuv=vu'-uv'v2

Q: If f(x) =2x2 - x3 , find f'(x) , f" (x), f"'(x) , and  f(4) x.Graph f , f' , f" , and f"' on a…

A: Given: f(x)=2x2-x3Differentiating f with respect to x  ⇒…

Q: 2) Find the derivative of the following func (c). f(x) = (x+ 7 sin z) (1 – 5 cos x) tanx (d). g(x) =…

A: We can find the answers as below.

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

A:

Q: Consider the following. f(x) = x In x6, (-1, 0) (a) Find an equation of the tangent line to the…

A:

Q: 5.6 Differentiate f with respect to t and g with respect to X, where

A: Let us start solving step by step....differentiate with respect to t and g with respect to x

Q: 1. Use the following formula (1) to evaluate derivative for each of the functions below: f(x+ h) -…

A:

Q: 1. Find the derivatives for the following functions. A.f(x) x3 (3 Inx – 1) - 9

A: A) f(x)=x39(3 lnx-1) f'(x)=19ddxx33 lnx-1       =19x3ddx3 lnx-1+3 lnx-1ddxx3   (since uv'=uv'+vu')…

Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOL'N): x²(x + 1),…

A:

Q: 2. Let g(x) = -3 vx. Using whatever rules for differentiation are appropriate, find g'(x). x2

A:

Q: Suppose f(-1) = 1, f'(-1) = 5, and g(x) = x³ f(x). The tangent line to g(x) at x = 1 is given by y =

A: The objective is to find the equation of tangent line .

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

A: Quotient rule of differentiation:…