Question

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

Answer 1

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

Explanation:

We Need the Quotient rule

`(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)`