DERIVATIVE OF NATURAL LOG OF SECX

We know the derivative of lnx, which is ¹⁄ₓ. And also, the derivative secx is secxtanx.

(lnx)' = ¹⁄ₓ

(secx)' = secxtanx

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

If y = ln(secx), find ᵈʸ⁄dₓ.

Let t = secx.

Then, we have

y = lnt

By chain rule,

Substitute y = lnt and t = secx.

Substitute t = secx.

Therefore,

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