$[20]4.$ Use the rules of differentiation from textbook sections $3\mathrm{.}3-3\mathrm{.}5$ to find the derivative in each case. Simplify answers; this includes writing them with no negative exponents. Also, use appropriate notation for the name of each derivative function. For example, if $z=w^3,$ then the derivative can be written as $d\frac{z}{d}w=3w^2,$ or $z^{\text{'}}(w)=3w^2,$ or $z^{\text{'}}=3w^2.$

a$)f(x)=3\mathrm{.}6-5\mathrm{.}4x5x^2-\frac{1}{3}{x}^4$

b$)h(x)=5e^{x}cos(x)$

c$)g(t)=\frac{5t^2}{3}\frac{3}{2t^4}$

d$)y=\frac{\sqrt[3]{x}}{2}\frac{3}{(\sqrt[\phantom{2}]{x}{)}^5}$

e$)w=\frac{r^3}{r^{3}7}$