Home
Class 12
MATHS
Differentiate (tanx)^(1//x) with respect...

Differentiate `(tanx)^(1//x)` with respect to `x` :

Text Solution

Verified by Experts

Given that,
`y=(tanx)^(1//x)`
taking `log` on both sides we get,
`=>log y =1/x log tanx`
taking derivative w.r.t x on both sides we get,
`=>1/y (dy)/(dx)=1/(xtanx)sec^2x -(log tanx)/x^2`
`=>(dy)/(dx)=(tanx)^(1//x) [sec^2x/(xtanx)-(logtanx)/x^2]`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

Differentiate y=tanx

Differentiate (sin^(-1)x)^(x) with respect to x:

Differentiate (x^(x))^(x) with respect to x:

Differentiate (1+cos x)^(x) with respect to x:

Differentiate (cos x)^(x) with respect to x:

Differentiate sin(m sin^(-1)x) with respect to x

Differentiate x^(1/x) with respect to x:

Differentiate x^(cos)^^((-1)x) with respect to x:

Differentiate (tan x-(1)/(3secx)) with respect to 'x'.

Differentiate sin(x^(2)+1) with respect to x: