$13\mathrm{.}2.$ Suppose that $F(x)=f^{-1}(\{g(x){\}}^2)$ and that the functions $f($which is one$-$to$-$one, and hence has its inverse$)$ and $g$ satisfy the following conditions:

$f(2)=9,f(9)=5,$

$f^{\text{'}}(1)=4,f^{\text{'}}(2)=3,$

$g(1)=3,g^{\text{'}}(1)=2$

Find $F^{\text{'}}(1).$

$13\mathrm{.}3.$ Suppose that $g$ is a function with $g^{\text{'}}(\frac{1}{2})=5.$ Let $f$ be the function defined by

$f(x)=g(2co{s}^2(x)).$

Compute $f^{\text{'}}(\frac{}{3}).$