I'm trying to figure out this equation.(adsbygoogle = window.adsbygoogle || []).push({});

[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?

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# Partial Derivative

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