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Find the derivative of cos^(-1)(2x^(2)-1...

Find the derivative of `cos^(-1)(2x^(2)-1)" w.r.t. "sqrt(1-x^(2))" at "x=(1)/(2).`

Text Solution

Verified by Experts

The correct Answer is:
4
`"Let "y=sec^(-1)((1)/(2x^(2)-1))and z= sqrt(1-x^(2))`
Put `x= cos theta. ` Therefore,
`y=sec^(-1) (sec 2theta)=2theta and z=sqrt(1-cos^(2)theta)=sin theta`
`therefore" "(dy)/(d""theta)=2, (dz)/(d""theta)=c os theta or (dy)/(dz)=(2)/(cos theta)=(2)/(x)`
`"At "x=(1)/(2), (dy)/(dz)=4`
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