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Question

Find dydx if y=(x+1x)x

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Solution

y=(x+1x)x

logy=xlog(x+1x)

Differentiating both sides, w.r.t x we get

1ydydx=log(x+1x)+x×1x+1xddx(x+1x)

1ydydx=log(x+1x)+x2x2+1(11x2)

1ydydx=log(x+1x)+x2x2+1(x21x2)

1ydydx=log(x+1x)+x21x2+1

dydx=ylog(x+1x)+yx21x2+1

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