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: If f(-1) = 4 and f'(x) ≤ 5 for all x, what is the largest possible value of f(6)?

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

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

A:

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

A:

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)

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Q: If f(x) = (x² +2) e², what is f'(x)?

A:

Q: Let h(x) = f(x) = g(x). If f(x) = 9x² and g(x) = 8x, what is h'(-5)? - Do not include "h' (-5) =" in…

A: SOLUTION-

Q: Let f(x)=9cosx−4tanx f′(x)=    f'(7π/6)=

A:

Q: If h(x) = V5 + 4f(x), where f(1) = 5 and f'(1) = 2, find h'(1). h'(1) =

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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: 1. Find f'(x) for f(x) = ln x + 2e - 3x².

A: The given function fx=ln x+2ex-3x2. We have to find the derivative function f'x.

Q: dy + ydx %3D 3x²y?dx,

A: Given differential equation is bernaulli's differential equation.,  and we can solve it by reducing…

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

A: c.

Q: Suppose F(3) = 2, F(8)= -19, and F"(x) = f(x). —13, and G'(x) = g(x). Also suppose G(3) =0, G(8) = =…

A: use integration  for finding the values.

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…

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

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Q: Question #1112 percent of U.S. residents are in their thirties. Consider a group of eight U.S.…

A: X: Number of . residents are in their thirtiesNown= number of residents in group=8p=P(in their…

Q: If h(x) =/4+3f(x), where f(1) = 7, and f'(1) = 4, find the value of h'(1).

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

A:

Q: If fx)=5x-1, g(x)=1/x, and h(x)=g(fx)), then what is h'(0)?

A: Given that h(x)=g(f(x)) Using chain rule we get: h'(x)=g'(f(x))f'(x) We plug x=0 So,…

Q: 5. If f(x) = 2x² e*, find ƒ '(1).

A: Explanation of the answer is as follows

Q: If x f(x)+x g(X)= sin x, for nonzero x, then f''(X) + g''(x) is %3D

A:

Q: Provide the General Solution of each differential equations. Box your

A: Introduction: The equation dydx=f (x,y) of two variables x and y with its function f(x,y) defined on…

Q: If we let f(x) = 1-4x/1+4x What are.... f’(5) = f”(5) = f”’(5) =

A: we have to find derivative at that point

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: What is the set N of all natural numbers?

A: Set of all integers: ℤ={.......,-3,-2,-1,0,1,2,3.......} Set of all positive integers…

Q: If f(x) = (x+1)/(x-1), where x # 1, determine f '(1). %3D

A: derivative of fx=x+1x-1 at x=1

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: