If `x^(p) y^(q) = (x + y)^((p + q)) " then " (dy)/(dx)=` ?

Explanation

`x^(p)y^(q)=(x+y)^(p+q)`
take log on both sides, we get
`plog x+q log y = (p+q)log(x+y)`
differentiate w.r.t. x
`(p)/(x)+(q)/(y)(dy)/(dx)=(P+q)/(x+y)(1+(dy)/(dx))`
`(dy)/(dx)((q)/(y)-(p+q)/(x+y))=(P+q)/(x+y)-(p)/(x)`
`(dy)/(dx)((qx-py)/(y(x+y)))= (qx-py)/(x(x+y))`
`(dy)/(dx)=(y)/(x)`
Hence proved .