Question

Can someone explain what is going on here?

Answer 1

Post whenever you are ready.

Answer 2

I need to know this for a quiz tomorrow, but im not sure what it is. I think it might be directional derivatives? I just need to know what it is so I know what to study.

Answer 3

looks like an application of the chain rule

Answer 4

Yeah it's chain rule. Changing the subject from x to t

Answer 5

so, chain rule and parameterization?

Answer 6

hmm maybe you can call it that. ;D

Answer 7

Oh I see what he did now.

Answer 8

\[\frac{ du }{ dt }=\frac{ du }{ dx }\frac{ dx }{ dt }+\frac{ du }{ dy }\frac{ dy }{ dt }\]

Answer 9

So he just took the derivative with respect to t for the parameterized function, then took the partial derivative with respect to x and y, multiplied that by the derivative of the parameterized function by chain rule, then just plugged in for x