(Discrete Math - Induction) 'Formula Differentiation'

Hi all! I've got this problem in my set:

'1 + 2q + 3q^2 + ... + nq^(n-1) = [1 - (n+1)q^n + nq^(n-1)]/[(1 -
q)^2], q <> 1.

Estabilish [the formula above] by differentiating the expansion of the
formula for the sum of a geometric progression.'

I've been thinkering with this one all day, no clue on how to start.
ANY hints on how the derivative of the sum of terms of a G.P will get
into this are welcome.
.

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