Question

\[z=3x^2\cos({\pi}xy)-3y^2\sin({\pi}x^2y)\\{x(t)=2t^2+1}\\{y(t)=3e^{2t}}\]
calculate:
\[{dz \over dt}\Bigr|_{t=0}\]

Answer 1

What is the problem with this exercise?

Answer 2

so to dz/dt means take the derivative of z. and for that you would have to use chain rule and product rule..

Answer 3

ohh but it has to be t. ummm.

Answer 4

my guess would be to plug x(t) and y(t) in the corresponding x and y of your z equation.

Answer 5

\[\frac{dz}{dt}=\frac{\partial z}{\partial x}\frac{dx}{dt}+\frac{\partial z}{\partial y}\frac{dy}{dt}\]