Question: Partial Derivatives, Symbolic Matrix

I'm pretty new to Maple. I've been using MATLAB for quite a while but it isn't very convenient for this problem. My first question is if it's possible for Maple to do partial derivatives for a function with two variables. Here's an example of what I am doing.

W = Q*qA - P(qA - (qA-qE)/2) - (1/2)*k1*(qA - (qA-qE)/3)^2 - (1/2)*k2*(qA - 2(qA-qE)/3)^2;

(Maple cleans that up quite nicely)

Now I want to take the partial of W with respect to qA as well as the partial of W with respect to qE. So I should get something like this:

dW = Q*dqA - P(dqA - dqE)/2 - ...

I was wondering if Maple could do something like that. What I have been doing is this:

dWqA = diff(W,qA);

dWqE = diff(W,qE);

...Which is fine but dW also equals to zero which means you'll need to separate the dqA terms from the dqE terms.

=> dW = [Q - P/2 - .... ]dqA + [P/2 - ....]dqE = 0

I don't know if Maple is capable of separating the terms in that way. Next step is if dW = 0, then:

[ Q - P/2 - .... ]  = 0  (this will have qA and qE terms)

[ P/2 - ...] = 0 (this will also have qA and qE terms)

So once we move our constants Q and P/2 to the other side, what we will eventually have is this:

[2x2] * [2x1] = [2x1]

And we must solve for qA and qE. Maple can solve for symbolic matrices, but I'm wondering if Maple can separate the variables from each other. I know I could separate by hand, but I'm just curious if Maple can do it for me.

Since for this problem, it feels like I'm already doing most of the work by hand and it seems like the only thing I even use Maple for is to solve the symbolic matrix. Feels like I'm doing it the long way.

Anyone has any idea or does this sound confusing?