If $\displaystyle u=f(x,y)$, where $\displaystyle x=e^scos(t)$ and $\displaystyle y=e^ssin(t)$, show that

$\displaystyle \partial^2u/(\partial*x^2)+\partial^2u/(\partial*y^2)=e^-^2^s[\partial^2u/(\partial*s^2)+\partial^2u/(\partial*t^2)]$

Printable View

- Nov 11th 2010, 12:30 PMdesperatestudentmultivariable chain rule proof
If $\displaystyle u=f(x,y)$, where $\displaystyle x=e^scos(t)$ and $\displaystyle y=e^ssin(t)$, show that

$\displaystyle \partial^2u/(\partial*x^2)+\partial^2u/(\partial*y^2)=e^-^2^s[\partial^2u/(\partial*s^2)+\partial^2u/(\partial*t^2)]$ - Nov 11th 2010, 03:37 PMKrizalid
$\displaystyle \displaystyle\frac{\partial u}{\partial s}=\frac{\partial u}{\partial x}\frac{\partial x}{\partial s}+\frac{\partial u}{\partial y}\frac{\partial y}{\partial s}.$

think you can take it from there? - Nov 11th 2010, 04:28 PMdesperatestudent
how do i do the second derivative of the partial derivative?