# Math Help - Help with partial derivative needed

1. ## Help with partial derivative needed

I have a function
u(r,t)= (sin(kr-wt))/r

How do I find the partial derivatives:

du/dr
d^2u/dr^2
d^2u/dt^2

2. ## Re: Help with partial derivative needed

$u(r,t)= (sin(kr-wt))/r$

for $\frac{du}{dr}$

treat "t" as a constant, and then find derivative.

so

we find:

$\frac{du}{dt}(r^{-1}sin(kr-wt))= -r^{-2}sin(kr-wt)+r.r^{-1}cos(kr-wt)$
$= cos(kr-wt)- \frac{sin(kr-wt)}{r^{2}}$

Now from there solve the rest...