We know the derivative of lnx, which is ¹⁄ₓ. And also, the derivative sinx is cosx.
(lnx)' = ¹⁄ₓ
(cosx)' = -sinx
We can find the derivative of ln(cosx) using chain rule.
If y = ln(cosx), find ᵈʸ⁄dₓ.
Let t = cosx.
Then, we have
y = lnt
By chain rule,
Substitute y = lnt and t = cosx.
Substitute t = cosx.
Therefore,
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