1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x + cos²x 5) f(x) = cos(3x4 - 5x) +/- xtanx 6) f(x) x+ cos x x−sinx

Q: Let ƒ'(x) = ƒ'(2) = f(x) = (x³ + 4x + 8) ²

A: f(x)=(x3+4x+8)2 d dx(xn)=nxn-1d dx(constant)=0

Q: Let f(x)= (x^3+3x+2)^2 f'(5)= ?

A:

Q: f'(c)=f(b)-f(a)/b-a .Use the Mean Value Theorem to find the number c for the function f(x)=x3-3x+2…

A:

Q: = (1) cotr 1+csc.x

A: We will find the required.

Q: Let ƒ'(x) = f¹(e³) = ƒ(x) = (ln x)8

A: f(x)=(lnx)8 d dx(lnx)=1xd dx(xn)=nxn-1lne=1

Q: v=(*++1)(r+2) 11. (u)=(1+ \u)(u-u°)

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

Q: f'(x) = +6) ¹¹(™). Find f'(x). Let f(x) = (x³ + 6)¹(x).

A:

Q: Let z +1 f(x) x + 10 f'(- 7) =

A:

Q: f6) =V20x (?,) f'G) f'(x)

A:

Q: =2 Find f'cx) if f(x)= x²+1

A:

Q: Find the derivative of the function. y = x 5 Vx3+7 O y'=- 2VX3+7 3x7 5x3 Vx3 +7 3x6 O y'=. 5x4 Vx3…

A:

Q: (0,F) (L.F) (L+ F, 0) (L+F+ LF, 0) 2. The following is the graph of f'(x).

A: From the graph,when 0≤x≤L, f'x=F Therefore, f(x)=∫f'xdx=∫F dx=Fx+cc being an integrating constant…

Q: Compute f’(-2) using shortcut rules. f(x) = 5x + 9

A:

Q: 1 th X +7 Fy =

A:

Q: Exercise 5 Derivative Suppose f (x) = 12x-1. What is f'(x)?

A: GUIDE: (1) Derivatives (a) Power Rule dxd​(xn)=nxn−1  EXERCISE 5Step 1: Write the given f(x)=12x−1…

Q: 77. er = 1+ x20 + 20 +...

A:

Q: Find the first derivative f' and the original function f. f"(x) = x³ - 12x, ƒ'(1) = 0, ƒ(1) = 10

A: Topic - Differential equations We are given f''(x)=x3-12x ,f'(1)=0 ,f(1)=10 ∫xndx=xn+1n+1+C

Q: determine f given f' and a point which statify f. f'(X)= 4x3-3x2+2x (3,80)

A: To determine f given f' and a point which statify f.   f'(X)= 4x3-3x2+2x (3,80)

Q: Find मिव x) e -e e* + eX

A:

Q: Find all functions ƒ whose derivative is ƒ'(x) = x + 1.

A: Given that f'(x)=x+1

Q: Exercise 7 Derivative of the sum Suppose y = 5x³ + 8x - 1. What is dy/dx?

A:

Q: Find the increasing and decreasing intervals of the function f'(x)= -3/(x-1)2. Then find the local…

A: f'x=-3x-12

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

A: fx=4x2+3x+3 Now,…

Q: Find the derivative of f(x). ƒ(x) = 3xª sec(x) ƒ'(x) =

A: To find the derivative of the following function.

Q: Find f. f "(x) = x-2, x > 0, f(1) = 0, f(7) = 0 f(x) =

A:

Q: Let f(x) = = f'(x) = = /3x² + 3x + 2 2

A:

Q: y = Vx* X

A:

Q: Let f(x) = f'(x) = = x+6 x +3 6

A:

Q: find f'tx w/ や

A: Explanation of the solution is given below...