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## Homework Statement

[tex]T(x,t)[/tex]

What is the fourier transform of

[tex]

\frac{1}{x}\frac{\partial T}{\partial x}

[/tex]

[tex]

F(\frac{1}{x}\frac{\partial T}{\partial x}) = \int^{\infty}_{-\infty} \frac{1}{x}\frac{\partial T}{\partial x} e^{i \theta x}dx = ??

[/tex]

## Homework Equations

## The Attempt at a Solution

Can this be split up using convolution into...

[tex] F(\frac{1}{x}\frac{\partial T}{\partial x}) = F(\frac{1}{x})F(\frac{\partial T}{\partial x}) =\int^{\infty}_{-\infty} \frac{1}{x} e^{i \theta x}dx \int^{\infty}_{-\infty} \frac{\partial T}{\partial x} e^{i \theta x}dx

[/tex]