Let $f(x,y)=xy^{2}$ and $c(t)=\left(t^{2},2t^{3}\right)$

(a) Calculate:
$\nabla f \cdot c'(t)=$

(b) Use the Chain Rule for Paths to evaluate $\frac{d}{dt}f(c(t))$ at $t=1$.
$\frac{d}{dt}f(c(1))=$