Function
$$𝐴(𝑥,𝑦)=2𝑥𝑦 − i\cdot 𝑥^2𝑦^3.$$
I need to perform some operations on this function, starting with finding its gradient.
One way would be to take the partial differential of the function w.r.t $x$ and ignore the partial wrt to $y$. In that case the outcome would come out to be:
$$2y – 2ixy^3$$
Is this approach correct?
Furthermore i need to calculate, the divergence of the given function. How would i go about that?
Best Answer
You should apply the definition directly: $$\nabla f(x,y)=\begin{pmatrix}\partial_x f(x,y)\\ \partial_y f(x,y)\end{pmatrix}.$$
Yes, indeed, your partial derivative with respect to $x$ is correct.
Again, the definition of divergence is all you need.