# Math Help - Help with partial deratives

1. ## Help with partial deratives

I have to show that $u_{xx} = u_{t}$

for $u(x,t) = \frac{1}{\sqrt{4\pi t}} exp(\frac{-x^2}{4t})$

For $u_{xx}$, I got $u_{xx}= \frac{exp(\frac{-x^2}{4t})}{4 \sqrt{\pi} t^\frac{3}{2}} (\frac {x^2}{t} -1})$

and for $u_{t}$, I got $u_{t}= \frac{exp(\frac{-x^2}{4t})}{4 \sqrt{\pi} t^\frac{3}{2}} (\frac {x^2}{2} -\frac{1}{t^2})$

Is either derivative correct? I think I am close but cant quite figure where I am going wrong.

2. ## Re: Help with partial deratives

The correct answer is uxx = ut = [exp(-x2/4t)/4sq. root pi *t3/2] * (-1 + x2/2t).

Basically something is going wrong within the brackets of your answer. Check those.

3. ## Re: Help with partial deratives

If you want to check your intermediate result,

$u_x=-\frac{xe^\frac{-x^2}{4t}}{4 \sqrt{\pi} t^\frac{3}{2}}$

I got the same answer as mrmaaza123 for $u_{xx}$ and $u_t$.

- Hollywood

4. ## Re: Help with partial deratives

the two answers above are correct if you are looking for some help on it.. wolfram math have a nice applet to get partial derivatives and also shows the workings.

5. ## Re: Help with partial deratives

Can anyone show me the steps in solving $u_{t}$?

I have $u_{xx}$ now - thanks to you all!

6. ## Re: Help with partial deratives

For $u_t$. Use the product rule to get:

$u_t=\frac{1}{\sqrt{4\pi t}}\frac{x^2}{4t^2}e^{-\frac{x^2}{4t}}-\frac{1}{4\sqrt{\pi}t^{3/2}}e^{-\frac{x^2}{4t}}$ then factor out an $\frac{e^{-\frac{x^2}{4t}}}{4\sqrt{\pi}t^{3/2}}$ and then your left with the correct $u_t$ Hope this helps. p.s in the first product dont forget that $\sqrt{4\pi t}$ $4t^2= 8\sqrt \pi t^{5/2}$