d If g(x): ªſ^*[e'− In(2t+1)]dt, find g''(x) . dx -2 A B == 4 (2x + 1)² 4 (2x + 1)² None of the given choices E) e*. De-In(2x+1) 2 (2x + 1)²

Q: In (x) (#3) S@ dx

A: Consider the given integration as Use the formula of integration as

Q: Question 8 The team installing the conveyor belts has a measuring tape in imperial units. Determine…

A: To convert the given length in feet.

Q: = In (2x) + cos (6x)

A:

Q: If f(x) In 2 + e9x find f '(0). f '(0) = | 9/2

A:

Q: dx -= In(F (x))+C. What is F (/3) if C=0? For (x+x³) (xtan-'(x) + 1)

A:

Q: point(s)  (6.1,y) is/are on the circle  x2+y2=49. Determine the missing coordinate(s) and enter the…

A:

Q: Suppose that f(2) = -3, g(2) = 2, f '(2) = -4, and g'(2) = 5. Fir (a) h(x) = 5f(x) – 4g(x) h'(2) =…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: If 4 – x2 f(x): 2 + x2 find f' (x). f' (x) =

A: Given function is Differentiating both sides with respect to x by using quotient rule of…

Q: If f( x)= e² + 2x , what is f'(x) ? O f'(x)=e" +2 O f'(x)= e2 + 2 O f'(x)= e" – 2 O f'(x)= e

A:

Q: Suppose f(x) and f'(x) have the following values. -5 -4 -3 -2 -1 f(x) 8 10 15 16 14 f'(x) -2 -3 9 -5…

A: We need to find  out h'(-5).

Q: If f(x) = In( 1 + e4x), find f '(0). f '(0) =

A: The objective is to find f'(0).

Q: Evaluate 2x+4 1. fx e**dx 2. SInx dx 3. J x2-2x 4.(a) (e* + 1)2 dx, (b) Sx³e2x dx.

A:

Q: Find f' where f(x) = ln(x²-2x)

A: We have to find  for the following functionWe know that

Q: Find 1 h'(1) if h(x) = g(f(x)), g(x h'(1) = = x + 1 X-1 and f(x) = In(x).

A:

Q: 3. Find f'(x). 2 f(x) = In x + 3e - 2x

A: given,  f(x)=lnx+3ex-2x2

Q: Suppose F(7) = 3, F(10) = -6, and F'(x) = f(x).

A:

Q: 4. If f(x) = 7x - 3+ In x, then f'(1) = (A) 4 (B) 5 (C) 6 (D) 7 (E) 8

A:

Q: 1 64 + 4f(1) + 7z²(f(x))* = 0 and f(1) = -2, find f'(1).

A: Given:

Q: '5 '5 '5 If f(x) dx = 33 and g(x) dx = 14, find [2f(x) + 3g(x)] dx. %3D

A:

Q: 7. If y = e*², then d²y dx2 boins9 (A) (2x)(x² – 1)e*²-2 stod beniu (B) ex2 (C) 2xe*2 (D) (2 +…

A:

Q: 8. (a) Show that (b) Evaluato 1/3 3 √1+9x² -4x4 dx dx = ln(1 + √2).

A:

Q: 5. If f(x) = 2x² e*, find ƒ '(1).

A: Explanation of the answer is as follows

Q: (a) E (e + log4 (7)) = 6*x^5*e^x^6 %3D dr (6) (()) - [ d da

A: We will use chain rule to don't the derivative.

Q: Let f(x) = x* – 7e*. (a) f' (-1) = (b) f" (-1) =

A: Given function is  fx=x4-7ex Here f'x and f''x are first and second derivatives respectively So…

Q: Find h' (2) given that f(2) = -3, g(2) = 4 , f (2) = -2 and g ' (2) = 7 such that h (x) = f (x) *g…

A: The solution are next step

Q: if f(x)=(x^2+4x+2)^2 find f'(x) and f'(1)

A:

Q: x) [in(3x²-36)]². Then f'(x) = A. 12x In (3x²-36) 3x²-36 O A. O B. O C. O D. O E. 2 In (3x²-36)…

A:

Q: Find h'(x) given that h(x) = Vx² +1

A: To do this problem we need chain rule  Chain Rule (using ’ ) f'(g(x))= f’(g(x))  g’(x) We will use…

Q: If f(2)=1, f'(2)=5, g(2)=2, and g’(2)=-3, then d *) |x=2

A: Given,          f2=1, f'2=5 , g2=2 and g'2=-3

Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: Suppose H(x) = f(g(x)) and %3D f(14) = 3 f' (2) = 13 g(14) = 2 d (14) = 4 Find H' (14)

A: Chain rule of differentiation: