6. Find \( f'(-2) \) given the following:

\( g(-2) = -3 \) and \( g'(-2) = 5 \)
\( h(-2) = 1 \) and \( h'(-2) = -4 \)

\( f(x) = (g(x))^2 h(x) \)






Answer is: option2

\( -66 \)

Solution:

\( f(x) = (g(x))^2 h(x) \)

\( f'(x) = (g(x))^2 h'(x) + h(x) \left[ 2g(x) g'(x) \right] \)

\( f'(-2) = (g(-2))^2 h'(-2) + h(-2) \left[ 2g(-2) g'(-2) \right] \)

\( f'(-2) = (-3)^2 (-4) + (1) \cdot \left( 2 \cdot (-3) \cdot (-5) \right) \)

\( f'(-2) = -36 - 30 \)

\( f'(-2) = -66 \, \text{Ans} \)

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