How do you use the chain rule to differentiate #f(x)=ln(cosx)#?

1 Answer
Pablocito
Jul 3, 2017
  • tan x

Explanation:

Derivative ln (cos x)
Note Derivative ln x = 1 / x
So Derivative ln (cos x) = 1 / cos x
But we must also take the derivative of the argument [cos x]
which is - sin x
Thus
Derivative Ln (cos x) = - sin x / cos x = - tan x

You can check this by Integrating -tan x
with U Substitution to obtain Ln (cos x)

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