DERIVATIVE OF NATURAL LOG OF SINX

We know the derivative of lnx, which is ¹⁄ₓ. And also, the derivative sinx is cosx.

(lnx)' = ¹⁄ₓ

(sinx)' = cosx

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

If y = ln(sinx), find ᵈʸ⁄dₓ.

Let t = sinx.

Then, we have

y = lnt

By chain rule,

Substitute y = lnt and t = sinx.

Substitute t = sinx.

Therefore,

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