(x^p /x^q)^p+q * (x^q /x^r) ^q+r *(x^r/x^p) ^r-p

Q. If $y=\frac{1}{1+x^{q-p}+x^{r-p}}+\frac{1}{1+x^{r-q}+x^{p-q}}+\frac{1}{1+x^{p-r}+x^{q-r}}$ then $\frac{dy}{dx}=$

Q. Prove that:
$[\frac{x^q}{x^r}{]}^{\frac{1}{qr}}\times [\frac{x^r}{x^p}{]}^{\frac{1}{rp}}\times [\frac{x^p}{x^q}{]}^{\frac{1}{pq}}=1$

Q. If $P\equiv (\frac{1}{x_p},p);Q\equiv (\frac{1}{x_q},q);R\equiv (\frac{1}{x_r},r),$ where $x_k(\ne 0)$ denotes the $k^{th}$ term of an HP for $kϵN$, then

Q. If $P\equiv (\frac{1}{x_p},p);Q=(\frac{1}{x_q},q);R=(\frac{1}{x_r},r)$ where $x_k\ne 0$ denotes the kth term of an HP for $kϵN$ then

Q. Evaluate: $\frac{x^p}{x^p+x^q}+\frac{1}{x^{p-q}+1}.$