Question

Question #b5d1e

Answer 1

`2xcscx - 2x^2cot2xcsc2x`

Explanation:

We can approach this using the quotient rule;

`y= x^2csc2x` = `x^2/(sin2x)`

hence quoteint rule; if `f(x)=u/v, then ,f'(x) = (vdu-udv)/v^2`

then `d/dx(x^2/(sin2x)) = (sin2x*2x - x^2*2cos2x)/sin^2(2x)`

as `d/dx( sinlamdax ) = lamdacos(lamdax)`

Hence simplifying to give;

`dy/dx = 2xcsc2x - 2x^2cot2xcsc2x`