Let f(3) = 1, g(2) = 3, f'(3) = 4, g'(2) = 5. If h(x) = f(g(x)), ﬁnd h'(2).
My professor got 20 for this. Why would you ignore g(2)?
Wouldn't it be 4*3 * 5?
Because the chain rule is f'(g(x)) * g'(x)
$\displaystyle h(x) = f[g(x)]$
$\displaystyle h'(x) = f'[g(x)] \cdot g'(x)$
$\displaystyle h'(2) = f'[g(2)] \cdot g'(2)$
note that $\displaystyle g(2) = 3$ is substituted into the $\displaystyle f'$ term ...
$\displaystyle h'(2) = f'(3) \cdot g'(2)$
$\displaystyle h'(2) = 4 \cdot 5 = 20$