# How should I do partial derivatives in Maple in a symbolic way?

I want to calculate the partial derivatives of the function $$A(x,y)$$. For example, I want to use Maple to calculate $$\frac{\partial^2}{\partial x\partial y}\left(K\cdot x\cdot A(x,y) \right)$$ where $$K$$ is some constant. Here the function $$A(x,y)$$ is not defined explicitly and so I expect to see terms like $$\frac{\partial^2}{\partial x\partial y}A(x,y)$$ in the answer.

I used the following Maple code to calculate

D[1,1] (K * x * A) (x,y) assuming K::constants

However, Maple will treat $$x$$ in $$K \cdot x \cdot A$$ also as a function. How should I tell Maple that $$x$$ is a variable that I want to take derivative with?

• D takes operator as an argument, diff takes expression as an argument. I guess you could use either D[1,2]((x,y)->K * x * A(x,y))(x,y) or diff(K * x * A(x,y),[x,y])
– Sil
Jan 2, 2023 at 23:19

Judging by the partial result you're expecting $$\frac{\partial^2}{\partial x\partial y}A(x,y),$$ I'm assuming you're looking to make use of $$D[1,2]$$ (refering to the first and second variable). We can define $$f$$ as $$f:=(x,y)\to K\cdot x\cdot A(x,y).$$ From here you get the desired output $$D[1,2](f)(x,y) = K\cdot \frac{\partial}{\partial y}A(x,y) + K\cdot x\cdot \frac{\partial^2}{\partial x\partial y}A(x,y).$$ You can at any point convert to partials with $$\mathrm{convert}(\%,\mathrm{diff})$$.