Problem 3. Let fn(x) = x^ (ln(x) – Hn). fn+1(2) [ fn(x) dx = Show that n+1 Remark: Note that fo(x) = ln(x), so the functions fn(x) are "higher order antiderivatives" of ln(x). + C.

Q: y"+y' - 2y = x2

A: Solution :-

Q: If f(x) + x2[f(x)]ª = 18 and f(1) = 2, find f '(1). %3D f '(1) =

A:

Q: D. f(x) = In x + 2e - 3x2

A:

Q: Evaluate the expression a+b a+b when a=23a=23 and b=45b=45. Write in simplest form

A: # the expressions are printed twice , taking them once given a=23 and b=45 The value of a+b is as…

Q: 4. Let f(x) = e3h(x) and g(x) = h(e3"). Find f'(7) and g'(2) given that h(7) = 2, h'(7) = 4, h'(e) =…

A: We have to find

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

A:

Q: Let h(x)=f(x)/g(x). If f(x)=−cos(x) and g(x)=4x^2+2x−3, what is h′(x)?

A: Given,          hx=fxgx. And fx=-cosx  and  gx=4x2+2x-3.

Q: 3. Given f(4) = 1, f'(4) = 3, g(4) = -2, g'(4) = -5. %3D %3D If h(x) (2x3+1)f (x) Vxg(x) calculate…

A: Given that, hx=2x3+1fxxgx Differentiating with respect to x we get,…

Q: 6. Let f(x) = -5x¹ and g(x) = 2x + x. If h is the function defined by h(x) = f(g(x)), which of the…

A:

Q: 6- y = f(x) 5. 4 3. y = g %3D 2)

A:

Q: 14) Is f(x) = ln(x²) + 1 odd, even, or neither? You must show you work.

A: Given query is to find function is odd even or neither.

Q: If f(x) = x cosh then f'(9) = 1 ¹() x²-9

A: The given function is

Q: Find f''(x). f(x) = (x² + 1) * %3D f"(x)=

A: We have to solve

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

A:

Q: LET 9 (3)=4₁ g (3)=-1 FIND H (3) For H(X) = xg(x) 5x-6 FUNCTION

A: solution is given below..

Q: If f(x) + x²[f(x)]³ = 10 and f(1) = 2, find f '(1). f '(1) =

A: Given:  f(x) + x2 [f(x)]3 = 10 and f(1) = 2

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

A:

Q: GeoGebrä Task 1: This rectangle has been decomposed along its diagonal. Recompose the two pieces to…

A: A rectangle is a closed quadrilateral with four sides and four angles. All the four angles of the…

Q: If g'(8)= 6 and h'(8)= 17, find f'(8) for f(x) = ,9(x) f'(8) = (Simplify your answer.)

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: Evaluate f'(x) at x =2 given f(x) = (x² – 3)ª A B 2 © 1 none of the given choices E 4

A:

Q: 1. Find f(x) if f'(x) = x/x and f(1) = 2

A: Given that: f'(x)=xx and f(1)=2

Q: 1. If h(x) = (f(x))² – (g(x))² , f' (x) = -g(x) and g' (x) = f(x), then h'(x) = (a) 0 (b) –4f(x).…

A:

Q: 1. f(x) = 6x + 15 find f'(x) Answer:

A:

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: If f(x) = f'(2) 3x + 1 x + 1 then:

A: given  f(x)=3x+1x+1dxndx=nxn-1d dx(ab)=b(dadx)-a(dbdx)b2

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:

Q: If f(x) = x° + x³ + x, find f ¯'(3) and f(f¯'(2)). %3D

A:

Q: f(x) = tanh(6x) then f'(x) =

A: