Partial derivative using only function notation

[Bman12345]

Homework Statement

I need to find the partial derivative of the following, with respect to x


q(x,y,e(x,y,u))
where e(x,y,u) is a function

Homework Equations

The Attempt at a Solution

Well, the problem is I don't have a clue how to solve using just the function notation - I'm used to doing it to an actual fuction (if that makes sence)

so I tried doing the chain rule,
(I will use d as I don't know how to get the patial derivative symbol)

$$\frac{d q(x,y,e(x,y,u)}{d e(x,y,u)}$$ $$\times$$ $$\frac{d e(x,y,u)}{d x}$$

However I do not think this is right. I don't think I use the product rule as it seems to be a function within a function, not two functions times together.

So yeah, what should be an easy problem has me stumped!

 

[lurflurf]

Use the chain rule, but it should be a sum.

[f(u(x,y,x),v(x,y,x),w(x,y,x))]_x=f^(1,0,0) u_x+f^(0,1,0) v_x+f^(0,0,1) w_x=f_u u_x+f_v v_x+f_w w_x

where raised (a,b,c) means differentiate slot 1 a times, slot 2 b times, and slot 3 c times
I assume x,y,u are independent variables.