What is the derivative of $ln ({sin}^{2} x)$ $ln(sin^2x)$ ?

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Answer 1 · 2018-05-11T16:10:06

Use chain rule
$f (x) = h (g (x))$ $f(x)=h(g(x))$
$f'(x)=h'(g(x)) g'(x)$

$ln(sin^2(x))$

$(ln(sin^2(x)))'=$
$=1/(sin^2(x))*(sin^2(x))'=$

$=1/(sin^2(x))2*(sin(x))*(sin(x))'=$

$=2/(sin(x))*(cos(x))=2/tan(x)=2 cot(x)$

What is the derivative of ln(sin^2x)ln(sin2x) ln(sin^2x)?