Answer
a) f'(5) = 6 + 18 = 24
b) Not possible to answer (Need g'(3))
c)f'(5) = $\frac{4}{3}$
d)f'(5) = 162
Work Step by Step
a)
f'(x) = g(x)$\times$h'(x) + h(x)$\times$g'(x)
f'(5) = g(5)$\times$h'(5) + h(5)$\times$g'(5)
f'(5) = -3$\times$-2 + 3$\times$6
f'(5) = 6 + 18 = 24
b)
f(x) = g(h(x))
f'(x) = g'(h(x)) $\times$ h'(x)
f'(5) = g'(h(5)) $\times$ h'(5)
f'(5) = g'(3) $\times$-2
Since we do not know g'(3), it is not possible to solve this question.
c)
f(x) = $\frac{g(x)}{h(x)}$
f'(x) = $\frac{(h(x)\times g'(x)) - (g(x)\times h'(x))}{h(x)^{2}}$
f'(5) = $\frac{(h(5)\times g'(5)) - (g(5)\times h'(5))}{h(5)^{2}}$
f'(5) = $\frac{(3 \times 6) - (-5 \times -2)}{9}$
f'(5) = $\frac{(18) - (10)}{9}$
f'(5) = $\frac{8}{9}$ = $\frac{4}{3}$
d)
f(x) = g(x)$^{3}$
f'(x) = 3$\times g(x)^{2}$ $\times g'(x)$
f'(5) = 3$\times g(5)^{2}$ $\times g'(5)$
f'(5) = 3$\times 9$ $\times 6$
f'(5) = 162
