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Answer 1 · 2017-10-29T15:28:36

#2xcscx - 2x^2cot2xcsc2x#

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#