Question

Rate of change

Answer 1

So lets say:
\[f(xy)=2x^3y\]
\[x=3t^2\]
\[y=2t\]

Answer 2

\[\nabla f _{x}=6x^2y\]
\[\nabla f _{y}=2x^3\]

\[\frac{ dx }{ dt }=6t\]
\[\frac{ dy }{ dt }=2\]

Answer 3

Then something something chainrule....

Answer 4

This is all with respect to t btw*

Answer 5

Please, include the instructions for each problem you post.