If $\left|x\right|<1\text{, then }\frac{d}{dx}\left[1+\frac{p}{q}x+\frac{P(p+q)}{\mathrm{\angle }2}{\left(\frac{x}{q}\right)}^2+\frac{p(p+q)(p+2q)}{\mathrm{\angle }3}{\left(\frac{x}{q}\right)}^3\dots \dots \mathrm{\infty }\right]=$

$(1-\mathrm{x}{)}^{-\mathrm{p}/\mathrm{q}}=1+\mathrm{p}(\mathrm{x}/\mathrm{q})+\frac{\mathrm{p}(\mathrm{p}+\mathrm{q})}{2!}(\mathrm{x}/\mathrm{q}{)}^2+\dots$

$\frac{d}{dx}\left[1+\frac{p}{q}x+\frac{P(p+q)}{\mathrm{\angle }2}{\left(\frac{x}{q}\right)}^2+\frac{p(p+q)(p+2q)}{\mathrm{\angle }3}{\left(\frac{x}{q}\right)}^3\dots \dots \mathrm{\infty }\right]=\frac{d}{dx}(1-x{)}^{-p/q}$

$\frac{-p}{q}{\left(1-x\right)}^{\frac{-p}{q}-1}\times \left(-1\right)=$$\frac{p}{q(1-x{)}^{\frac{p}{q}+1}}$