Home
Class 12
MATHS
Differentiate log sin x w.r.t. sqrt(x)....

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

Text Solution

Verified by Experts

`"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 )`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Solved Examples|28 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.1|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Differentiate log sinx w.r.t. sqrt(cosx) .

Differentiate x^(sinx) w.r.t. sinx

FInd the differentiation of x.sinx w.r.t. x .

Differentiate (x)/(sinx) w.r.t . sinx.

Differentiate sin^(2) x w.r.t. e^(cos x) .

Find the differentiation of sinu w.r.t.x.

Differentiate x^(sin x), x gt 0 w.r.t. x.

Differentiate (x)/(cosx) w.r.t . cosx.

Differentiate x^(sin^(-1)x) w.r.t 'x'

Differentiate the following w.r.t. x : sqrt((e)^(sqrt(x))),x gt 0 .