Monday, 8 July 2019

trigonometry - Why is this derivative incorrect?




We have to find the derivative of f(x)=tan(2x)sin(x)



I would like to know why my approach is incorrect:



f(x)=sin(x)2cos2(2x)tan(2x)cos(x)sin2(x)



=2sin(x)tan(2x)cos(x)cos2(2x)sin2(x)



=2sin(x)sin(2x)cos(x)cos3(2x)sin2(x)




p.s. - To avoid confusion ; I wanted to get rid of the tan. I'm sure there is a shorter method than this but I don't want it; I just want to know why this is wrong.


Answer



Third line is: 2sin(x)tan(2x)cos(x)cos2(2x)cos2(2x)sin2(x)
instead of 2sin(x)tan(2x)cos(x)cos2(2x)sin2(x)


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