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Question

Let y=sin1x then prove that (1x2)y2xy1=0. Where y1 and y2 are first and second order derivatives of y with respect to x respectively.

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Solution

Given,

y=sin1x

Now differentiating both sides we get,

y1=11x2

Now squaring both sides we get,

(1x2)y21=1

Now again differentiating both sides with respect to x we get,

(1x2)2y1.y22x.y21=0

or, (1x2)y2xy1=0. [ Since y10]

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