What is the derivative of $f (x) = ln (cos x)$ $f(x)=ln(cosx)$ ?

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Answer 1 · 2015-12-03T03:47:35

$- tan x$ $-tanx$

According to the Chain Rule, $d/dx[ln(u)]=(u')/u$ .

Therefore:

$f'(x)=(d/dx[cosx])/cosx=(-sinx)/cosx=-tanx$

What is the derivative of f(x)=ln(cosx)f(x)=ln(cosx)f(x)=ln(cosx)?