a)If h(x)=f(3x) then  h′(2) b) If  y=f(x2+2)  then  y′∣x=1= c) If  G(x)=cos(f(x)) then  G′(π)=

Q: If f(x) = tan (3x), then f'(x) = (A) 12 tan (3x) sec?(3x) (B) 4 tan (3æ) sec2(3x) (C) 12 tan (3x)…

A: derivative

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) = (x² +2) e², what is f'(x)?

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Q: Let ƒ (x) = x³ – 5x² – 8 and let g be the inverse of f (i.e. g (x) = f -1 (x).

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Q: 5. Use the chain rule to compute the derivatives. a) f(x) = sin²x = (sin x)² b) f(x) = sin(x²) c)…

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Q: nd and simplify 2² x² (f(x) g(x)). O d² O −(ƒ (x) g(x)) = ƒ” (x) g(x)+ f (x) g″ (x) Hint 2² -(f(x)…

A: Given query is to find the double derivative.

Q: a) f(x) = x28 + e-x 2x + 13 b) h(x) = e³x³-4x²+2 + 5ln(x³3 -x+ eⓇx) c) y = x²2 (12x³ - 25x) 42

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Q: Which of the following is not equal to the derivative of y = (cos(x) – sin(æ))?? A 2 (2 sin? (x) –…

A: The given function is y=cosx-sinx2

Q: Find a function f(x) such that f'(x) = 9x² +2 and f(0) = 1 f(x) =

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Q: e8(x) and g(x) 43. Find f'(2) if f(x)

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(4) = 11, f(11) = 3, f'(11) = 8, f'(4) =…

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Q: If f(x) = cos-(r"), then f'(x) = (A) (B) (C) (D) (E) -32? sin-(æ³) (A) O (B) o (c) O (D) (E)

A: We have to find derivative

Q: If f(x) (1)? = 2 x² + 3x x+1 " then what is

A: Given: f(x)=x2+3xx+1

Q: Let F(x) = f(x5) and G(x) = (ƒ(x))5 . You also know that aª Then F'(a): = = = 8, f(a) = 2, ƒ'(a) =…

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Q: If f(x)=(x-2)(2x + 1)6, th en what is f'(O) ?

A: We will use the product rule and chain rule to find f'(x)

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: 12. Find the second derivative for the function f (x)=4x+12x²-20x-18 and solve the equation f"(x)=0.…

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Q: 2. If g(x) = (ƒ 03ƒ •4f)(x) = ƒ (3ƒ (4ƒ(x)). Determine gʻ(3), given f(3) = 1, ƒ(4)=1, ƒ'(3) = 2 and…

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Q: If f(x) = cos x, then f'() = A. B. - C. - C. D. √3

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Q: f(x) = sec x As x = π-/2, f(x) =  As x = π+/2, f(x) =

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Q: Differentiate the functions. a) f(x) = 2 – 3x + b) f(x) %3D Зе* + sinx c) f(x) = 3x

A: As per guidelines, we will solve only first three subparts. Kindly repost other subparts separately.