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Q.

If (x+y)m+n=xmyn then dydx=

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a

xy

b

−yx

c

−xy

d

yx

answer is D.

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Detailed Solution

(m+n)log⁡(x+y)=mlog⁡x+mlog⁡ydydx=−(∂f/∂x)(∂f/∂y)=−m+nx+y−mxm+nx+y−my=−[nx−my]⋅y(my−nx)x=yx
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If (x+y)m+n=xmyn then dydx=