(a) Let f(x) = cos(3x – 2). Find f"(x). (39) %3D (b) Let g(x) = 2***. Find g (153) (x). %3D

Q: The function f(x) = 3x³ + cos(3ræ) + 2x , x > 1 is known to be a strictly increasing function on its…

A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: Let f(x) = (sin(x))*. Find the value of (a) 1 (b) 2 (c) 2 (d) 2 (e) 0

A: The given function is fx=sinxx. To find the value of f'π2, first take the logarithmic of fx=sinxx on…

Q: 3. Find f. (a) f"(x) = x + 12x² %3D

A:

Q: dy dx (b) y = (x³ - 2x + 8) (x² + 4) 1. Use the Differentiation Rules to find (a) y = 6x³ + 3x√x -…

A: Since you have posted a multiple question according to guildlines I will solve first(Q1)   question…

Q: If f(x) = sin x 7T find f %3D (a) 1 (b) / 2 2. . т (c) 1– 4 (d) V2 1+ (e) /2 (1- 3)

A:

Q: 1.2 s Find first derivative for the following functions. dx (a) y = 5+ 6x + 4x3 (b) y = In(2x) +x*…

A: Note:-Since you have asked multiple questions, we will solve the first question with three sub-parts…

Q: Suppose F(x) = | cos(2?)dz. Find F'(x).

A: We have to solve the problem

Q: Let f(1) = 1, g(1) = -3,h(1) = 2, f'(1) = -1,g'(1) = 2, and h'(1 d f(x) g(x) dx h(x) Find when x =…

A: Please refer to the image below

Q: c If f" (x) = 18 cos 3x and f' (0) = f(5) = 1, find f(x).

A: The solution of the problem is given in the next step.

Q: -g(x) = x²sinx cosx . Find g'(x).

A: We will use the product rule of differentiation to find the derivative.

Q: f(æ) = a³ + 7x – 7, and f(2) = 15. Let g(x) be the inverse function of f(x). g'(15)

A:

Q: If f(x) = 18x2 + 96 3 ³√√x' find f'(8).

A: Given Function:- fx=18x23+96x3

Q: Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown F G…

A:

Q: Let Find f(x) = y = f(x) = 5x + 18 cos x. d f(x) =

A: Given query is to find the derivative at indicated point.

Q: 1 3. Let f (x) = 4x +- х Find f'(x) S f(x)dx а. b. Find

A: Here given as fx=4x+1x Differentiate as f'x=ddx4x+1x=ddx4x+ddxx-1=4-x-2=4-1x2

Q: If f(x) = cos x, then f'() = A. B. - C. - C. D. √3

A:

Q: Find f(2) if f (x) = e"

A: given equation f(x)=ex

Q: If f(x)= cos(4x) Plot the function from (x=0) to (x=180)

A:

Q: Find f such that f'(x) = 4x – 3, f(4) = 0. %3D %3D f(x) = D %3D

A: Given that: f'(x)=4x-3, f(4)=0

Q: Find f. (x + 1) f'(x) = (1) = 3 %3D f(x) =

A:

Q: Suppose that f'(x) = 3x² + 3 – 1 and f(1) = 3. Find a formula for f(x) and then %3D %3D use this…

A: Topic- integration

Q: Let f (x) = (10x + 6)(x – tan x). Then %3D - f'(x) =

A:

Q: The following figure shows the graph of f(x). It F' = f and F(0)=3, find F(4). f(x) 3 2 1 1 2 4 3

A: We have, F'x = fx F0 = 3 To evaluate: The value of F4

Q: 2. Find the derivatives: (a) f(x)=(x² - 2x+1) (x² -1) x+2x+5 (b) f(x): %3D x² +1

A: Part (a) Given a function Using product rule of the derivative

Q: f(x)=cos(x) Glx)こxや+1 d f(9(x) = t3 clx

A: We have to find derivative

Q: If f(x) = 4 cos(7 ln(x)), find f'(x). %3D Find f'(3).

A: Explanation of the answer is as follows

Q: (z2)juə = (x)/ sin(#x). Compute f'(x). %3D

A: We will solve the problem

Q: Find f if f"(x) = 2 + cos(x), f(0) = -10, f(x/2) = 4. %D %3D f(x) = iii

A: Recall: ∫xn dx= xn+1n+1+c; where c is an integration constant. ∫sinx dx= - cos(x)+c; where c is an…

Q: If f(x) = 3 cos(3 In(x)), find f'(x).

A: Consider the function  f(x)=3cos3ln(x)