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Question

d(sin1x)dx

A
1(1x2)
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B
1(1x4)
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C
1(1x3)
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D
1(1+x2)
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Solution

The correct option is A 1(1x2)
y=sin1x,
y+δy=sin1(x+δx)
(x+δx)=sin(y+δy)
dydx=limx01δx(sin1(x+δx)sin1x)
=limx0δysin(y+δy)siny=1cosy
=1(1sin2y)=1(1x2)
Note that when :δx0,δy also tends to zero.

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