How is the derivative of x \cos x \sin x \frac 12 \sin 2x+x \cos 2x? I tried using the pro

jelentetvq

jelentetvq

Answered question

2022-01-23

How is the derivative of xcosxsinx12sin2x+xcos2x?
I tried using the product rule on xcosx and got:
(xcosx)=xsinx+cosx
then I used the product rule to differentiate xcosxsinx and got:
(xcosxsinx)=(xsinx+cosx)sinx+(xcosxcosx)=xsin2x+sinxcosx+xcos2x

Answer & Explanation

Brenton Pennington

Brenton Pennington

Beginner2022-01-24Added 15 answers

Use, 2sinxcosx=sin2x
and
cos2xsin2x=cos2x
So that
x(cos2xsin2x)+sinxcosx=xcos(2x)+12sin(2x)
SaphypycleDapc5

SaphypycleDapc5

Beginner2022-01-25Added 11 answers

The two answers are equivalent:
xsin2x+sinxcosx+xcos2x=x(cos2xsin2x)+12sin2x=xcos2x+12sin2x

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