## Calculus 8th Edition

$p'(2)=42$
Notice that $g(t)=x$ and $h(t)=y$. We will use the Chain Rule to find $p'(t)$ and then find it for $t=2$: $$p'(t)=(f(g(t),h(t))'=f_x(g(t),h(t))g'(t)+f_y(g(t),h(t))h'(t)$$ So, $$p'(2)=f_x(g(2),h(2))g'(2)+f_y(g(2),h(2))h'(2)= f_x(4,5)\cdot(-3)+f_y(4,5)\cdot6=2\cdot(-3)+8\cdot6=42$$