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Question

If xy=yx, then find dydx.

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Solution

xy=yx.

Taking log on both sides

ylogx=xlogy.

Differentiating both the sides by uv rule

y.1x+logx.dydx=x.1ydydx+logy

yxlogy=xy.dydxlogxdydx

yxlogyx=dydx(xylogxy)

dydx=yxlogyxxylogxy

dydx=yx(yxlogyxylogx).

1212886_1435995_ans_6abd0261ccf5474db08cf261cf00268d.jpg

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