Finding the Gradient using Quotient Rule

[cse63146]

Find the gradient of F(s,t) = f(x(s,t), y(s,t)) where f(x,y) = y/x x = s^2 + t^2 y = s^2 - t^2.

I'm not sure how to even start the problem. Could someone point me in the right direction?

 

[HallsofIvy]

Do you know the chain rule for partial derivatives?

 

[cse63146]

Does it have something to do with this:

$$\frac{\partial F}{\partial s} = \frac{\partial F}{\partial x}\frac{\partial x}{\partial s} + \frac{\partial F}{\partial y} \frac{\partial y}{\partial s}$$

 

[HallsofIvy]

Yes, now DO it!

 

[cse63146]

Already did, and got the correct answer, thank you.