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Question

If xm.yn=(x+y)m+n, then dydx is


A

yx

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B

x+yxy

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C

xy

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D

xy

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Solution

The correct option is A

yx


xm.yn=(x+y)m+n
m ln(x)+n ln(y)=(m+n) ln(x+y)
Differentiating both sides.
mx+nydydx=m+nx+y(1+dydx)
(mxm+nx+y)=(m+nx+yny)dydx
mynxx(x+y)=(mynxy(x+y))dydxdydx=yx


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