# Implement "nested" derivatives and cylindrical coordinates?

Posted 3 months ago
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 Hello, I am looking to solve the PDE $$\frac{1}{r} \frac{\partial}{\partial r} \left( r \frac{\partial T}{\partial r} \right) = \frac{1}{\alpha} \frac{\partial T}{\partial t}$$ in Mathematica, but I can't figure out how to input the $\frac{\partial}{\partial r}\left( r \frac{\partial T}{\partial r} \right)$ part. Is it correct to nest the derivatives like below? (1/r) * D[r * D[T[r,t], r], r] - (1/\[Alpha][r]) * D[T[r,t], t] == 0 Furthermore, how do I indicate to Mathematica that I am working in cylindrical coordinates instead of Cartesian?Thanks.