It has been a long time since I've had to do derivatives so I'm rusty.

show that $\displaystyle \frac {\delta u}{\delta t} = k \frac {\delta ^2 u}{\delta x^2}$ where 'k' is constant.

$\displaystyle u=u(x,t)= exp(-n^2kt)sin(nx)$

I get :

$\displaystyle u_t(x,t)=-n^2k(1) exp(-n^2kt)sin(nx)$

and

$\displaystyle u_x(x,t)=exp(-n^2kt) ncos(nx)$

$\displaystyle u_(xx)(x,t)=exp(-n^2kt) (-n^2sin(nx))$

so if I multiply the second order derivative (U_xx) by 'k' then this should be correct?

I just want to make sure that since I'm doing partial derivatives with respect to x for the last 2 that I can ignore the $\displaystyle exp(-n^2kt)$ because it is all a cosntant. And when I do the derivative of $\displaystyle sin(nx)$ I only need to pull the 'n' out and change it to cos(nx). Also, for the first derivative with respect to 't' I am taking the '1' exponent off of 't' and bringing it forward.

Last semester was 100% integrals and I feel like I have to relearn the first semester all over. Thanks for the help.

Also, just notices that my $\displaystyle U_xx$ doesnt work. Anyone able to tell me how to get two sub x's in a row. Figured parathese would work, guess not.