Question

$x^p+\frac{\frac{q}{2}y^{2p-q}}{(xy^2)^ppq}$

Answer 1

$f(x,y)=x^p+\frac{\frac{q }{2}\times y^{2p−q}}{(xy^2)^p \times p q}$ $($ Where $y$ is a function of $x)$

$\frac{df}{d x}=px^{p-1}+$ $\frac{(xy^2)^p\times pq(\frac{q}{2}(2p-q)y^{2p-q-1}\frac{dy}{dx})-\frac{q }{2}\times y^{2p−q}(pq(x^p(2p)y^{2p-1}\frac{dy}{dx}+px^{p-1}y^2p)) }{((xy^2)^p\times pq)^2}$