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Differentiate log sin x w.r.t. sqrt(x)....

Differentiate log sin x w.r.t. `sqrt(x).`

Text Solution

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`"Let "u=tan^(-1)((sqrt(1+x^(2))-1)/(x))and v= tan^(-1) x.`
`(du)/(dx)=cos x and (dv)/(dx)=-(sin x)/(2sqrt(cos x))`
`"or "(du)/(dv)=(du//dv)/(dv//dx)=(cot x)/(-(sin x)/(2sqrt(cos x)))=-2sqrt(cos x cot x "cosec" x )`
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