Module 1 : A Crash Course in Vectors
Lecture 4 : Gradient of a Scalar Function

Example 15 :
Find the gradient of $ V = e^{-(x^2+y^2)}$in cylindrical (polar) coordinates.
Solution :
In polar variables the function becomes $ V =e^{-\rho^2}$. Thus

\begin{eqnarray*} \nabla V &=& \hat\rho\frac{\partial e^{-\rho^2}}{\partial\rho}\\ &=& \hat\rho e^{-\rho^2}.(-2)\rho = -2\hat\rho\rho V \end{eqnarray*}

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