## Laplace transform sqaured differential

Hi

I was wondering what the Laplace transform of a squared differential is.
With that I mean the Laplace of (y' )^2 (this being y'*y' and not the second order derivative). So for example velocity squared.
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 there is a lot of similarity between the Fourier Transform and the Laplace Transform. the F.T. is really just the L.T. with the real part of $s = \sigma + i \omega$ set to zero. try to answer the question regarding the F.T. and see if you can generalize.
 I don't know the exact form off the top of my head, but it will be an ugly convolution of the form: integral (s^2 F(a)F(a-s) da)

 Tags laplace derivative, squared