Assuming all indicated derivatives exist. d ff{x) g(x)] is equal to : dx h(x) ƒ f'(x) g '(x) h(x) – f(x) g(x) h '(x) h2(x) f(x) g(x) h '(x) – f '(x) g(x) h(x) – f(x) g '(x) h(x) h2(x) d [fx)] dx h(x)J d fg(x)] dx h(x)J f'(x) g '(x) h'(x) (f '(x) g(x) + f(x) g '(x)) h(x) – f(x) g(x) h '(x) h2(x) +

Q: Consider the function. f(x) = x R(x) + Q(x) Identify the derivative f'(x). f'(x) = xR'(x) + R(x) +…

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Q: If f(x) - g(x) = 1, then f and g have the same derivative. O True O False

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Q: (a) f(z) = (z³ + 2x + 1)(2 + ) 31 b) f(z) = VI +2 1 (c) f(x) = 2x² – I

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Q: Find the derivatives of the functions in Exercis y = (1 + 2x)e-2x

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Q: 3. Find the derivative of f (x) = 2x²e² tan x.

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Q: Consider the following functions. g(x) = x3 – x h(x) = (x3 – x)4 f(x) = 9(x3 – x)4 Find the…

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Q: The derivative of the function f (x) is represented by f (x, isf"(x) = A. D. B. E. C.

A: We have to find the derivative of the following function -  f(x) = 1x3

Q: f(x)Vx² f(x) = 10* 2 f(x) = (х+1)

A: We know that ddxxn = n·xn-1 ddxax = ax lna ddxuv = v·ddxu - u·ddxvv2

Q: 8) Find the derivative of the function f(x) = (2x-1 x² + 1 if x ≤0 if x>0

A: Step 1:   Step 2: Step 3: Step 4:

Q: Evaluate the derivative of y = (x 2+ 2x + 1)2usingd/dx (ƒ(g(x)) = ƒ′(g(x)) # g′(x)

A: We have to evaluate the derivative ofy = (x2+ 2x + 1)2usingddx(f(g(x))=f'(g(x))*g'(x)

Q: Let g(x) 10x + 12 3x + 6 Find the derivative of g'(x). g'(x) =

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Q: f(x) = x(=") – (x*)*, x > 0. – (2*)*, x > 0. %3D

A: We have to find the derivative of  f(x)=x(xx)-(xx)x ,  x>0

Q: Find the derivative of g(x) = 4x 1+4* •

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Q: Find the derivative of f (a) = e" (x² + 2).

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Q: f(x)=πcos⁡(πx).  Find the twentieth derivative of f(x)

A: After third derivative, the sign will become positive because of the Cosine and the coefficient will…