Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(3) and G'(3). F'(3) G'(3) = = f(3) = 9, ƒ(9) = 3, ƒ'(9) = 4, f'(3) = 15

Q: Let f(x) = (x³ + 3x + 7)3 f'(x) = f'(4) =

A: According to question given thatf(x)=(x3+3x+7)3

Q: x+f(x) g(x) then find h'(2). If h(x) =. and f(2) = 2, f'(2) = - 5, g(2) = 1, g'(2) = 0,

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Q: Let F(x) = f(x¹) and G(x) = (ƒ(x))ª . You also know that a³ = 14, ƒ(a) = 3, ƒ'(a) = 12, ƒ' (aª) =…

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Q: f(x)=(x2+3x+7)4, then f'(x) =    f'(1) =

A: We have to find derivative

Q: Let F(z) = f(f(2)) and G(r) = (F(x))'. You also know that f(3) = 12, f(12) = 3, f'(12) = 5, f'(3) =…

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(5) = 6, ƒ(6) = 2, ƒ'(6) = 6, ƒ'(5) = 12…

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Q: if f(2) = -3 , f'(2) = 4 g(2) =1 g'(2) = -5 then find F'(2) where F(x) = f(x) *g(x)

A: f(2)=-3, f'(2)=4, g(2)=1 and g'(2)=-5F(x)=f(x).g(x)

Q: If ƒ'(x) = (2x −— 3)² and f(3) = 5, then, f(x) = =

A: Topic - differential equations We are given, f'(x)=(2x-3)2 and f(3)=5we know that∫xndx =xn+1n+1+C

Q: Let f and g be the functions in the table below. g(x) 2 3 1 X 1 2 3 f(x) 3 1 2 (a) If F(x) =…

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Q: 5x+2x+3 f(x) = √x

A: f(x)=5x2+2x+3x

Q: Find a function ƒ(x) such that ƒ'(x) = −8x² + 1 and ƒ(0) = 1 ƒ(x) = |

A: f'(x)=-8x2+1f(0)=1∫xndx=xn+1n+1+c

Q: Let F(x) = f(r°) and G(r) = (f(x))° . You also know that a = 12, f(a) = 2, ƒ'(a) = 15, f'(aº) = 5…

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x   Given: Fx=fx9 ;…

Q: If f and g are functions that satisfy f'(2) = 5 and g'(2) = −2, find h'(2) for h(x) = 2f(x) - g(x) +…

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Q: i) n=1 1 1+2+3++n j) 1 n In n(ln(Inn)+1) k) 2" +n n!+1 n=1

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Q: If find f'(x). ƒ'(x) = | Find f'(4). ƒ'(4) = f(x) = = 7-x² 8+x²

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Q: Find F'(2) given that f(2) = 5, f'(2) = 6 , g(2) = -1, g'(2) = –7, and F(x) = f(x)g(x).

A: Given: f(2)=5f'(2)=6g(2)=−1g'(2)=−7andF(x)=f(x)g(x)

Q: f(9) = 2, f(2) = 3, f'(2) = 13, f'(9) = = 13 Find F'(9) and G' (9). F'(9) : G' (9) =

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Q: Let F(x) = f(x) and G(x) = (f(x))*. You also know that a³ = 12, ƒ(a) = 3, ƒ'(a) = 5, ƒ' (aº) = 8…

A: If we consider a function y which is a function of x only. Then, the derivative of y with respect to…

Q: If F(x) = f(g(x)), where f(-1) = 9, f'(-1) = 3, f'(5) = 4, g(5) = -1, and g'(5) = 8, find F'(5). %3D…

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Q: Suppose f''(x) = 42x + 16e-4x, ƒ'(0) - 14, and f(0) = - 9. Then f(x) =

A: See this solution in below.

Q: Suppose F(x) = f(x³), G(x) = (f(x))³ and: a² = 10, f(a) = 3, f'(a)=4, ƒ'(a³) = 8. Find:

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Q: f(g(x)), where f(1) = 3, f '(1) = 5, f '(2) = 5, g(2) = 1, and g'(2) = 5, find F '(2). If F(x) F…

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Q: Suppose f''(x) = 6x + 9e ƒ'(0) = - 8, and f(0) Then f(x) = = - - 3x - 5.

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Q: Suppose that Find f'(2). f'(2) = f(x) = = e³x x² + 4

A: Given f(x)=e3xx2+4   We are required to findf'(2)         The following formulas of derivatives has…

Q: If ƒ (x) +x5(ƒ (x) )² = 34 and f(1) = 2, then f'(1) =

A: Derivative

Q: Given f''(x) = 4x + 3 and f'(- 2) %3D -4 and f( — 2) Е — 2.

A: Given,          f''x=4x+3  and  f'-2=-4  and  f-2=-2.