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Question

Explain the differentiation of sin-1x.


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Solution

Explain the differentiation of sin-1x.

Let us assume that, y=sin-1x.

Thus, to get the differentiation of sin-1x, we need to find dydx.

Take Sine of both sides of the equation.

siny=sinsin-1xsiny=x

Differentiate both sides of the equation with respect to x.

dsinydx=dxdxcosy·dydx=1dydx=1cosy

It is known that, sin2x+cos2x=1.

As siny=x.

Thus, cosy=1-sin2y

cosy=1-x2

dydx=11-x2.

Therefore, the differentiation of sin-1x is 11-x2.


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