If then x^y=e^(x-y), then dy/dx at x =1 is …

Question

If then x^y=e^(x-y), then dy/dx at x =1 is ….

MARKS Content Team · Accepted Answer

Correct answer: (C) 0. Given have, x^y=e^(x-y) taking log on both sides, we get ylogx=x-yloge=x-y ….(i) when x=1,thenylog1=1-y ⇒y=1 On differentiating both sides, y1/x+logx.dy/dx=1-dy/dx ⇒dy/dxlogx+1=1-y/x ⇒dy/dxlogx+1=(x-y)/x ⇒dy/dx=(x-y)/(xlogx+1) when x = 1, then dy/dx=(1-1)/(1log1+1)=0

If then $x^{y} = e^{x - y},$ then $\frac{d y}{d x}$ at x =1 is ….

Solution

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If then xy=ex-y, then dydx at x =1 is ….

Solution

Relevant Questions

If then $x^{y} = e^{x - y},$ then $\frac{d y}{d x}$ at x =1 is ….