If m(x) = E[I(x)] is a composite function, then and I'(x) exist. O m'(x) = E[I(x)]I'(x) ○ m' (x) = E' [I'(x)]I'(x) O m'(x) = E' [I'(x)] Om'(x) =E[I'(x)] I'(x) O m'(x) = E' [I(x)]I'(x) , provided that E' [I(x)]

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

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

Q: If f(x) = 3x³ - 6e*, find: f'(x) = ƒ' (3) = ƒ''(x) = = f''(3) =

A: Given, f(x)=3x3-6ex

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: If f(x) = f' (x) for all æ, then f(x) = = f" (x) for all x. True False

A: f(x) = f'(x) for all x Then f(x) = f"(x)  for all x

Q: Find f'(x). f(x) = (9 + In x) f'(x) = O

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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: Find f'(x). 5 f(x) = (5x² + 1)² f'(x) = [

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Q: Let f(x) = e³x²(9x − 2). Compute f'(x). f'(x) =

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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: 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: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that ƒ(8) = 11, ƒ(11) = 2, ƒ'(11) = 5, ƒ'(8) =…

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Q: If g(2) = 3, g'(2) = 5, h(0) = 2, and h' (0) = 4 find F'(0). F'(0)

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Q: Let F(x) = f(f(xæ)) and G(x) = (F(x))² . You also know that f(9) = 3, f(3) = 2, f'(3) = 5, f'(9) =…

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Q: If f(x) = 5x² In(6x), then f'(x) = f''(x) = f'''(x) f(4) (x) = f (5) (x)

A: We have to find derivative of give function.

Q: Show that if f(x) is a function satisfying f'(x) = f(x)^2, then its inverse g(x) satisfies…

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Q: If f(x) = (x2 + 5x + 8)*, then f'(x) = f'(5) =

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Q: Let f(x)= 57+52+4 f'(x) = = f'(3) = =

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Q: If f(x) = xe"+æ") , then f'(x) = %3D (A) (e² + x³) x(e*+a°-1) (B) (e* + 5x4) In(x) xe"+x*) (C) (e* +…

A: See the details solution in below

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: Find T' (X). f(x) = (x²-3) (x²+7) f'(x) = (Type an exact answer.)

A: