Suppose that f(5) = 1, f '(5) = 8, g(5) = −4, and g'(5) = 2. Find the following values.(a)    (fg)'(5) (b)    (f/g)'(5) (c)    (g/f)'(5)

Question

Suppose that f(5) = 1, f '(5) = 8, g(5) = −4, and g'(5) = 2. Find the following values.(a)    (fg)'(5) (b)    (f/g)'(5) (c)    (g/f)'(5)
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Solution 1

(a) (fg)'(5)

This is the derivative of the product of two functions, which can be found using the product rule: (fg)' = f'g + fg'.

Substituting the given values, we get:

(fg)'(5) = f'(5)g(5) + f(5)g'(5) = 8*(-4) + 1*2 = -32 + 2 = -30

(b) (f/g)'(5)

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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