Give f(x,y) = sin (x-5t) find partial f/partial S and partial f/partial r
x = (s-6r)^2
t = e^(s^2+r)
Use the chain rule.
$\displaystyle \frac{\partial f}{\partial s} = \frac{\partial f}{\partial x}\frac{\partial x}{\partial s} + \frac{\partial f}{\partial t}\frac{\partial t}{\partial s}$
and
$\displaystyle \frac{\partial f}{\partial r} = \frac{\partial f}{\partial x}\frac{\partial x}{\partial r} + \frac{\partial f}{\partial t}\frac{\partial t}{\partial r}$