multivariable chain rule proof

• November 11th 2010, 01:30 PM
desperatestudent
multivariable chain rule proof
If $u=f(x,y)$, where $x=e^scos(t)$ and $y=e^ssin(t)$, show that

$\partial^2u/(\partial*x^2)+\partial^2u/(\partial*y^2)=e^-^2^s[\partial^2u/(\partial*s^2)+\partial^2u/(\partial*t^2)]$
• November 11th 2010, 04:37 PM
Krizalid
$\displaystyle\frac{\partial u}{\partial s}=\frac{\partial u}{\partial x}\frac{\partial x}{\partial s}+\frac{\partial u}{\partial y}\frac{\partial y}{\partial s}.$

think you can take it from there?
• November 11th 2010, 05:28 PM
desperatestudent
how do i do the second derivative of the partial derivative?