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\frac{\frac{\mathrm{d}}{\mathrm{d}x}(c)q^{2}-cq}{q^{2}}
Multiply q and q to get q^{2}.
\frac{q\left(q\frac{\mathrm{d}}{\mathrm{d}x}(c)-c\right)}{q^{2}}
Factor the expressions that are not already factored.
\frac{q\frac{\mathrm{d}}{\mathrm{d}x}(c)-c}{q}
Cancel out q in both numerator and denominator.
\frac{-c}{q}
Expand the expression.