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: Vx 3+x (g(x)) if g(x) = 3x +2 + S, * ** dx c) %3D

A: I applied Leibnitz rule

Q: If y=-2x² + sin x solve for the differential of dy.

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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: 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: (d) Use the following table to evaluate each derivative. I 0 1 2 f(x) 1 3 -2 g(x) f'(x) 1 2 4 -3 0.5…

A: Since you have posted multiple questions i can do first question as per our company guidelines,…

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: 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 f and g be functions that satisfy f'(2) = -6 and g'(2) = 9. Find h'(2) for each function h given…

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Q: Let f(x) and g(x) be functions whose graphs are shown below. Which of the following statements…

A: We are asked about the derivative of the function h given a graph of the functions f and g. Note…

Q: Find the derivative (x) = 2 In x – Vĩ

A: Given: fx=2lnx-x   As we know that; The sum/difference rule:  f±g'=f'±g' The Power law; ddxxn=nxn-1…

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

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

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Q: p(x) = (-2x)f(x), q(x)= f(g(x)), r(x)= 31 Use the table to find the derivative values. f(x) %3D

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