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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

`t/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)`
Taking log on both sides , we get
` p log x + q log y = (q + p) log (x + y)`
`rArr (p)/(x) + (q)/(x) (dy)/(dx) = ((p+q))/((x + y))(1 + (dy)/(dx))`
` rArr ((p)/(x) - (p+ q)/(x+y) ) = ((p+ q)/(x+y)- (q)/(y))(dy)/(dx)`
`rArr (dy)/(dx) = (y)/(x)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -MHT CET CORER
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