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

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

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

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

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

Help please!