d If g(x) = - S* [e'− ln(2t+1)]dt, find g''(x) dx -2 2 A ex. (2x + 1)² 4 (В B et + (2x + 1)² Ⓒe* -In(2x+1) 4 (D) e¹+ (2x + 1)²

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

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

Q: Differentiate: f(x) = 2ª + e² + log, 5 f'(x) = 2" In 2+ e² A 1 ® f'(x)= 2" +e² + : 1 © f'(x)= 2" +…

A:

Q: if f(x)=2ln(6+x) f'(x)= f'(3)=

A: Here, f(x)=2 ln (6+x)

Q: Find h'(2) if h(x) = In(x + Vx? – 1).

A: The given function is hx=lnx+x2-1. Evaluate the derivative of the given function as follows.…

Q: Find f'(x) for f(x) = e5a+2x

A:

Q: Find g'(4) given that f(4) = 3 and f '(4) = −5. g(x) =√x  *f(x))

A: f(4)=3, f'(4)=-5g(x)=sqrt(x). f(x)find g'(4).

Q: Let f(x) = |=| ƒ' (5). 0= √x-4 √x +4 Find f'(x).

A:

Q: f(x) = ln(cos3(2x+1)5)     f'(x) = ?

A: Given that f(x) = ln(cos3(2x+1)5)

Q: Find f'(x). f(x)= 4 Inx + e× − 5x² - f'(x) = [

A:

Q: (c) Let h(x) = . Find h'(1). f (x) (d) Let h(x) =2f(x)+g² (x). Find h'(4).

A: c.

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: et ● t'(x) = 805x4 (x),1 O %3D O t'(x) = 80(e)-(e*)(5x4) (x),1 e2r e2x ((*(-(,r5)(,2) 08 = (x),1 C…

A:

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

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

Q: f(x)= 7tan-1(5sin(4x)) f'(x)=?

A: We have to find the derivative of the given function f(x)= 7tan-1(5sin(4x)).

Q: If h(x) h'(1) = 25 = 3+2f(x), where f(1) = 3 and f'(1) : × = 5, find h'(1).

A:

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: Suppose f(2) = 4, f' (2) = 5, f(8) = 8, f' (8) = 2, g(2) = 4, g' (2) = -6, | dH and H(x) = f(x² +…

A: Topic :- Derivative

Q: Ex. 8 Differentiate k(x)= ln(x)f(x)

A: Our AIm is to differentiate the function given below:-f(x)=ln (x) f(x) -(i)

Q: If f(x)= 2x' +2/x+3ln x , then f'(1)= %3D

A:

Q: Find f'(x). f(x) = -14 Inx+ 5x². -7 f'(x) =

A: We will find the required derivative.

Q: Suppose y(t) = c1 e^(-t) [1 -1] c2 e^(t) [ 1 1], with the initial condition y(1) = [0 2]. Find c1…

A:

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: If f (x) = e2" (x³+1), then f' (1) =

A: The function is given by fx = e2xx3+1 To evaluate : The value of f'(1)

Q: Find h(x) if h'(x)= h(x): 5x (6-x²)² X and h(1) = -6.

A: NOTE: Refresh your page if you can't see any equations. . here we have take integration on both…

Q: f(x)=5ln(5+x)

A:

Q: Find h' (2) given h (x) = ƒ (x) g (x and given -3, f' (2) = 5, and gʻ (2) = 1 f (2) = 3, g (2)

A:

Q: 9x Find the derivative of the function f(x)=In x2+15 2x O f'(x)= x²+15 15-x2 f"(x)= x2+15 2x O…

A:

Q: Solve for k:  y(t) = y(0) * e^(kt* (1-t/p) )  (we know that y(0)=P/10)

A: We have given yt=y0·ekt·1-tp,  y0=p10 By dividing both sides of the equation by y(0), yty0=ekt·1-tp…

Q: Suppose f'(x)=√√/1 + 2x¹. d da -f(8x): d dx f(2x¹) = [

A: