How do you differentiate $ln(cos^2(x))$ ?

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Answer 1 · 2018-05-29T08:17:27

$-2tanx$

$d/dx[ln(cos^2(x))]$

Differentiate,

$1/(cos^2(x))*d/dx[cos^2(x)]$

Differentiate second term,

$1/(cos^2(x))*-2sinxcosx$

Multiply,

$-(2sinxcancel(cosx))/(cos^cancel(2)(x))$

Simplify,

$-(2sinx)/(cosx)$

Refine,

$-2tanx$

Answer 2 · 2018-05-29T10:03:20

As above

Alternatively, you could say:
$ln(cos^2(x)) = 2ln(cosx)$

Then:
$d/dx(ln(cos^2(x)))$
$= 2*d/dx(ln(cosx))$
$= 2* (-sinx)/cosx$
$= -2tanx$

How do you differentiate ln(cos^2(x))ln(cos^2(x))?