Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of x.

Question

Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of x. Find the derivative with respect to x of the given combination at the given value of x.

X f(x) g(x) f'(x) g'(x)

3 1 4 6 5

4 3 3 2 4

f(g(x)), x = 4

MULTIPLE CHOICE

6

18

-24

-8

Answer 1

Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of x. Find the derivative with respect to x of the given combination at the given value of x.

X f(x) g(x) f'(x) g'(x)

3 1 4 6 5

4 3 3 2 4

Find the derivative of: f(g(x)), x = 4 <== that is: (f(g(4))^' = ??

MULTIPLE CHOICE: (A) 6 (B) 18 (C) -24 (D) -8

Detailed Solution:

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(f(g(4))^' = f^'(g(4)) * g^'(4) <== Derivative Chain Rule

= f^'(3) * g^'(4)

= 6 * 4

= 24 <== (C) (Note: The -ve is typo, there no any -ve in this problem)