5. Let \( f(x) = x \cdot g(h(x)) \) where \( g(4) = 2 \), \( g'(4) = 3 \), \( h(3) = 4 \), and \( h'(3) = -2 \). Find \( f'(3) \).






Answer is: option2

\( -16 \)

Solution:

\( f'(x) = 1 \cdot g(h(x)) + x \cdot g'(h(x)) \cdot h'(x) \)

\( f'(3) = g(h(3)) + 3 \cdot g'(h(3)) \cdot h'(3) \)

\( f'(3) = g(4) + 3 \cdot g'(4) \cdot (-2) \)

\( f'(3) = 2 + 3 \cdot 3 \cdot (-2) \)

\( f'(3) = 2 - 18 \)

\( f'(3) = -16 \, \text{Ans} \)

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