7. Find \( f'(-1) \) given the following:

\( f(x) = \frac{(g(x))^2}{h(x)} \)






Answer is: option2

\( -28 \)

Solution:

\( f(x) = \frac{(g(x))^2}{h(x)} \)

\( f'(x) = \frac{h(x) \cdot (2 \cdot g(x) \cdot g'(x)) - (g(x))^2 \cdot h'(x)}{(h(x))^2} \)

\( f'(-1) = \frac{h(-1) \cdot (2 \cdot g(-1) \cdot g'(-1)) - (g(-1))^2 \cdot h'(-1)}{(h(-1))^2} \)

\( f'(-1) = \frac{(1) \cdot (2 \cdot 2 \cdot (-3)) - (2)^2 \cdot (4)}{(1)^2} \)

\( f'(-1) = -12 - 16 \)

\( f'(-1) = -28 \) Ans

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