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

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Answer 1 · 2015-12-08T14:45:50

$f'(x) = 1/x + cot x$

$f = ln (uv)$

$f' = 1/(uv) * (u'v + uv')$

$u = x Rightarrow u' = 1$

$v = sin x Rightarrow v' = cos x$

$f' = (sin x + x cos x) / (x sin x)$

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