What is the derivative of $\frac{ln (x)}{sin (2 x)}$ $ln(x)/sin(2x)$ ?

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Answer 1 · 2018-07-10T19:51:08

$f'(x)=(sin(2x)-2xln(x)*cos(2x))/(x(sin(2x))^2)$

$(u/v)'=(u'v-uv')/v^2$
and

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

so we get

$(1/x*sin(2x)-ln(x)*cos(2x)*2)/(sin(2x))^2$
multiplying numerator and denominator by $x$ we get

$(sin(2x)-2xln(x)*cos(2x))/(x*(sin(2x))^2)$

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