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Question

Find the derivative of [ln(tanx)]2.


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Solution

Find the required derivative.

Given function: [ln(tanx)]2.

Differentiating with respect to x, we get,

ddx[ln(tanx)]2=2ln(tanx)ddxln(tanx)ddxfxn=nfxn-1ddxfx=2ln(tanx)×1tanx×sec2xddxlnfx=1fxddxfx=2ln(tanx)×cosxsinx×1cosx2=2ln(tanx)×1sinx×1cosx=2ln(tanx)cosecxsecx

Hence, the derivative of [ln(tanx)]2is 2ln(tanx)cosecxsecx.


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