if x/(x-y) = log(a/(x-y) )
prove that
dy/dx= 2 - x/y

We havexx-y=logax-yxx-y=loga-logx-y                              As, logmn=log m- log nDifferentiating both sides, with respect to x, we getx-yddxx-x ddxx-yx-y2=-1x-y ddxx-y           As, ddxloga=0x-y-x1-dydxx-y2=-1x-y 1-dydxx-y-x1-dydx=-x-y 1-dydxx-y=-x-y+x 1-dydxx-y=y 1-dydx1-dydx=x-yy=xy-1-dydx=xy-2dydx=2-xy.

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