Partial Derivative

dimensionless

I'm trying to figure out this equation.

[tex]
{\Psi} = Ae^{-a(bx-ct)^2}
[/tex]

I've expanded this to

[tex]
{\Psi} = Ae^{-ab^2x^2-abxct-ac^2t^2}
[/tex]

When I try to find the derivative I get this

[tex]
\left(\newcommand {\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } }

\pd{\Psi}{t}{}\right)_x = (-2ac^2t-abxc)Ae^{-ab^2x^2-abxct-ac^2t^2}
[/tex]

I should get this instead

[tex]
\left(\newcommand {\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } }

\pd{\Psi}{t}{}\right)_x = (-2abcx-2ac^2t)Ae^{-ab^2x^2-abxct-ac^2t^2}
[/tex]

Can anyone tell me where my error is and how I can fix it?

krab

Try again in expanding
[tex](bx-ct)^2[/tex]