Question A$3(2$ marks$)$

Let

$F(t)=f(u(v(w(t))),p(q(r(t))))$

where

$f(x,y)=x^3-y^3,u(z)=e^z,v()=\sqrt[\phantom{2}]{+2},w(t)=sin(t)$

and

$p(s)=s^2,q()=ln(1+),r(t)=t^3$

Compute $\frac{dF}{dt}$ using the chain rule carefully.

Evaluate $\frac{dF}{dt}$ at $t=0.$