If Xmyn=x+ym+n, Then The Value Of Dydx Is - BYJU'S

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If xmyn=(x+y)m+n,thenthevalueofdydx is

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The correct option is C yxxmyn=(x+y)m+nTakinglogbothsides,weget⇒mlogx+nlogy=(m+n)log(x+y)Differentiatingbothsidesw.r.t.x,weget⇒mx+nydydx=(m+n)(x+y)(1+dydx)⇒(ny−m+nx+y}dydx=m+nx+y−mx⇒(nx+ny−my−nyy(x+y)}dydx=(mx+nx−mx−my(x+y)x}⇒nx−myy(x+y)⋅dydx=nx−myx(x+y)⇒dydx=yx

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