W= [ru/(1+ v)][1+ q] (the parentheses are crucial).
To find the partial derivative with respect to r we treat all other variables, u, v, and q, as constants.
So we can write it as W= Ar where A= [u/(1+ v)][1+ q]. The derivativae of Ar is A.
So the partial derivative of W with respect to R is [u/(1+ v)][1+ q].
Similarly, taking the partial derivative of W with respect to u we can treat it as W= Au with A= [r/(1+ v)]{1+ q] now.
So the derivative of W with respect to u is [r/(1+ v)][1+ q].
Taking the partial derivative of W with respect to v we can treat it as W= A/(1+v) with A= [ru]{1+ q] now.
The derivative of A/(1+v)= A(1+ v)^{-1} with respect to v is -A(1+ v)^{-2}.
So the derivative of W with respect to u is -[ru/(1+ v)^{-2}][1+ q].
Taking the partial derivative of W with respect to q we can treat it as W= A(1+q) with A= [ru]/(1+ v) now.
The derivative of A(1+ q) with respect to q is A
So the derivative of W with respect to u is [ru]/(1+ v).
