Gradients

[ffrpg]

Here's the problem. Find the gradient of f(x,y). f(x,y)=(x^2)e^-2y.


I don't have the solution to this and I need to know if I got the right gradient (I have more problems that depend on this gradient, points on it). I ended up getting, gradient f=<2xe^-2y, 2x-2e^-2y>. I don't think it's right, but can someone help me out here?

[StephenPrivitera]

No.
grad f= fx(x,y)i + fy(x,y)j
fx(x,y)=(2x)e-2y
fy(x,y)=(-2*2x)e-2y

[HallsofIvy]

Sorry, Stephen, you have fy wrong.

The derivative of e-2y with respect to y is -2 e-2y The other factor, x2 is independent of y so treat it like a constant fy= (x2)(-2e-2y)= -2x2e-2y.

The gradient of 2xe-2y is the vector <2x e-2y, -4xe-2y>.

What ffrpg wrote: f=<2x^e-2y, 2x-2e^-2y> may be typos or just carelessness: x^e-2y doesn't make much sense and in "2x-2..." you MEANT (2x) times (-2), not 2x subtract 2...

[StephenPrivitera]

Ah yes. Where is my head?