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Question

If y=sin1x1x2, 1<x<1 then (1x2)dydx equals to

A
x+y
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B
1+xy
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C
1xy
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D
xy2
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Solution

The correct option is B 1+xy
y=sin1x1x2

We have,
ddx(uv) =uddx(v)(v)ddx(u)v2

dydx=1x2×11x2(sin1x)121x2×(2x)(1x2)
(1x2)dydx=1+sin1x1x2×x
(1x2)dydx=1+xy

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