Question

Use the chain rule to find ∂f/∂s and ∂f/∂t for a dierentiable function f(x, y) where x(s; t) = s^2- t^2
; y(s, t) = st:

Answer 1

http://www.math.hmc.edu/calculus/tutorials/multichainrule/

Answer 2

Thank you for your kind assistance

Answer 3

So we have some function \(\large f(x,y) \qquad = \qquad f\left(x(s,t),y(s,t)\right)\)

Taking the partial derivative with respect to s gives us,\[\large \frac{\partial f}{\partial s} \qquad = \qquad \color{royalblue}{\frac{\partial f}{\partial x}}\cdot \frac{dx}{ds}+\color{royalblue}{\frac{\partial f}{\partial y}}\cdot\frac{dy}{ds}\]

Hmmm, they didn't tell us what \(\large f\) is. So I don't think you can do anything with those blue terms.

Answer 4

Oh our x and y are written in terms of 2 variables, i should have probably wrote partials for those chain rules :( Ugh my bad...