Question 8 8. Given f(x) =(3x² + 4x)(x –5). Which of the following is TRUE for f'(x)? (3x° +4x)(6x + 4) +(x° –s)(3x*) A (3x +4x)(3x²)-(x² – s)(6r +4) B (3x° +4x)(3x')+(x² –s)(6x+4) C (3x² + 4x)(ór+ 4)-(x² -s)(3x* ) D O A В

Q: Consider the function f (x) = 6x² + 4x + 2. Find F(x) so that F' (x) = f(x). %3|

A: f(x)=6x2+4x+2To find: F(x) such that F'(x)=f(x)

Q: Question 14 4. If f (x)= ,then f '(x) equals (1+3x)5 60 A (1+3x) 25 60 (1+3x) 10 - 60 (1+3x) 10 - 60…

A:

Q: 3x-4 -,x < 1 x+2 4. Given the function f (x) = . Calculate f'(1-) and f'(1+). In?x x+1

A:

Q: Let h(x) = 3x² + x -x² + 3x - 3 what is h' (2)?

A: We need to find out h'(2).

Q: If f(x) = (5x +7)°, then the value of (f-1 (x))' at (f(-1),-1) is

A:

Q: If f(t) = (t + 7t + 3) (5t² + 6), find ƒ'(t). Find f'(5).

A: Given : ft = t2 + 7t + 35t2 + 6

Q: 3x10 + 3a5 + 5æ² + 7. What particular solution that satisfies Suppose f'(x) 455 -? 66 f(1)

A:

Q: If f(x) = x² m2. find f'(2).

A: We will use simple differentiation rules to solve these questions.

Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

Q: f f(x)=- X+1 2x+1 1 = (2x + 1)²* 1 (2x + 1)² O 3x+1 (2x+1)²* 3x+1 O (2x + 1)² then f'(x) =

A: Topic: derivatives

Q: The function f is defined by ƒ (x) = -2x³ – x – 5 and f(-1) = -2. If g(x) = f¯1(x), what is the…

A: Given fx=-2x3-x-5f-1=-2Therefore, f-1-2=-1Differentiate with xf'(x)=-6x2-1f'-1=-7

Q: Find f. f(x) = 3 f'(x) = √√√x³ + ³√√x + 5ex + sec² x, f(0) = 8 4

A:

Q: Find the third derivative of f(x) = 3√x³-5cosx. 45 O f(x)= 4553 9 O f(x)= - O f(x)= 45 O f(x)= - 9…

A: It can be written as f(x)=3x3/4-5Cos(x)

Q: f(x) = 3x cos ƒ'(x). -1 (2x + 4) − √√/19 − 3x², find

A: Given: fx=3xcos-12x+4-19-3x2. To Find: f'x.

Q: Find the approximate integral of the following function using Simpson's 3/8 rule and determine the…

A: Given: fx=ex2, x=0, 4, E=0.0002 To find: n To find: Approximate integral.

Q: Suppose that f(x) 2 4x Find f'(x).

A: use quotient rule for differentiation

Q: Question 5 x3+5 Determine f '(x). f (x) = (A 1- 10x-3 B 3x2 3 2 (D 5x4 + 10x 2.

A: Given: fx=x3+52   As we know that; The sum./difference rule: f±g'=f'±g' The Power law; ddxxn=nxn-1…

Q: Let f(x)=√4x² + 4x + 6 f'(x) = f'(5) =

A: To find f'(x)

Q: If f(t) = (t + 5t + 4) (2t² + 2), find f'(t). Find f'(3).

A:

Q: I don't really understand the question below Given f(x) with f(1) = 2 and f′(1) = 5, find (a):…

A:

Q: 6x3 + 5x* + 3x Suppose that f(x) = Evaluate each of the following: x3 f'(-4) = f'(1) = %3D

A:

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

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

Q: Suppose f(-4)= -7 and f'(-4)= 7. Find t d (7x² + 10x + 3) f(x) at x = -4 is dx d f(x) dx 7x² + 10x…

A:

Q: 2. Determine the exact value of f'(2) for f(x) = (2e³ + 3e-6x)5.4,

A:

Q: / = 20. Evaluate f (a+ 2) for f(a) 3 4x-8'

A:

Q: Question 14 (2) + h(x)]dr 8 1.5 -2/6 -7 -6 Blank 1:

A:

Q: If f(x) = x' – 8x + 2, find f (-4).

A: We have,  fx=x3-8x+2           ⋯⋯1

Q: If f(x)=(x-2)(2x + 1)6, th en what is f'(O) ?

A: We will use the product rule and chain rule to find f'(x)

Q: 10. Find function that satisfies the given conditions: f"(x)=6x³-3x+4, f'(1)=-3, f(1) = -6

A: The function satisfies the condition f''x=6x3-3x+4, f'(1)=-3, f(1)=-6 use the integration formulas,…

Q: Given f(x) = x + 4, x < 0. Find (f-1)' (5) 10 1 2 | 29

A:

Q: Provide the table of signs for both f' and ff'.

A: Given function is fx = x+334x-12 = x4 +12x-1+16x-12 +114. Also, given that f'x = x-9x+324x-13    and…

Q: Find h'(x) given h(x) = 6x√√x. 3 O ○ 6x² 09√x 6x7 6+x7² None of these

A:

Q: 3-5x 11. Find f'(x), if (i) f (x) = (x² – 1)(x5 + 2)+/3, and (ii) f (x) (x3+2)1/3*

A:

Q: If f(x) + x²[f(x)]4 = 18 and f(1) = 2, find f'(1). f'(1) =

A: Given

Q: Suppose Im(f(z)) = 6x(2y -1) and f(0)= 3 -2i, f(1) = 6- 5i. Find f(1 + i)

A: Complex function

Q: Find ƒ′(x) if ƒ(x) = 15e3x

A: Given information: fx=15e3x