Compute the $\displaystyle q $-derivative and the $\displaystyle h $-derivative of $\displaystyle f(x) = x^n $.

So $\displaystyle D_{q}x^n = \frac{(qx)^n-x^n}{(q-1)x} = \frac{q^n-1}{q-1}x^{n-1} $. Also $\displaystyle D_{h}x^n = \frac{(x+h)^n-x^n}{h} $.

Is this correct?