Tính: $\frac{dz}{dt}$ nếu $z=e^{2x+3}$,trong đó $x=cost,y=sint$

Lời giải:

$\frac{dz}{dt}=\frac{\partial{z}}{\partial{x}}.\frac{dx}{dt}+\frac{\partial{z}}{\partial{y}}.\frac{dy}{dt}=2e^{2x+3y}.(-sint)+3e^{2x+3y}cost=e^{2x+3y}.(3cost-2sint)$