$(3)($a$)7pts$ Let $f$ and $g$ be functions defined on $R$ such that $g$ is the inverse function of $f.$ Let

$h(x)=\frac{g(x{)}^{g(x)}}{e^{g(x)}}$

Find $h^{\text{'}}(a),$ assuming that

$f(e)=a,f^{\text{'}}(e)=b$

for some constants a and $b.$

$($b$)7pts$ Let

$y(x)=\frac{e^{ta{n}^4(ln(x^5))}arcsi{n}^4(\sqrt[\phantom{2}]{x^{3}lnx})}{(sinx{)}^{sinx}}$

Find $y^{\text{'}}(x)$ using logarithmic differentiation.