DERIVATIVE OF NATURAL LOG OF TANX

We know the derivative of lnx, which is ¹⁄ₓ. And also, the derivative tanx is sec²x.

(lnx)' = ¹⁄ₓ

(tanx)' = sec²x

We can find the derivative of ln(tanx) using chain rule.

If y = ln(tanx), find ᵈʸ⁄dₓ.

Let t = tanx.

Then, we have

y = lnt

By chain rule,

Substitute y = lnt and t = tanx.

Substitute t = tanx.

Therefore,

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