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If x^(p) y^(q) = (x + y)^((p + q)) " the...

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

A

`y//x`

B

`py//qx`

C

`x//y`

D

`qy//px`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `x^(p)y^(q)=(x+y)^(p+q)`
Thinking log on both sides, we get
`p log x+q log y=(p+q)log (x+y)`
`implies(p)/(x)+(q)/(y)(dy)/(dx)=((p+q))/((x+y))(1+(dy)/(dx))`
`implies((p)/(x)-(p+q)/(x+y))=((p+q)/(x+y)-(q)/(y))(dy)/(dx)`
`implies(dy)/(dx)=y/x`
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