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Question

Differential coefficient of sin-1x w.r.t.cos-11-x2 is


A

1

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B

2

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C

11+x2

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D

none of these

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Solution

The correct option is A

1


Explanation for correct option:

Step-1: Differentiate the sin-1x with respect to x.

Let the given, u=sin-1x

dudx=11-x2..........i

Step-2: Differentiate the cos-11-x2 with respect to x.

Let the given, v=cos-11-x2

put, x=sinθθ=sin-1x

v=cos-11-sinθ2v=cos-1cosθv=θv=sin-1x

Differentiate with respect to x.

dvdx=11-x2...........ii

Step-3: Divide equation i by equation ii.

dudxdvdx=11-x211-x2dudv=1

Hence, correct answer is option A.


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