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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]`
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