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Question Number 54663 by Mikael_Marshall last updated on 08/Feb/19

$$y=cos2t\times sen2t$$$$$$$$y^{\prime }=?$$

Commented by maxmathsup by imad last updated on 08/Feb/19

$$y\left(t\right)=cos\left(2t\right)sin\left(2t\right)\Rightarrow y^{{}^{\prime }}\left(t\right)=-2{sin}^2\left(2t\right)+2{cos}^2\left(2t\right)=2({cos}^2\left(2t\right)-{sin}^2\left(2t\right))$$$$=2cos\left(4t\right).$$$$anotherwaywehavey\left(t\right)=\frac{1}{2}sin\left(4t\right)\Rightarrow y^{{}^{\prime }}\left(t\right)=\frac{4}{2}cos\left(4t\right)=2cos\left(4t\right).$$

Answered by peter frank last updated on 08/Feb/19

$$y^{{}^{\prime }}=2\cos 4t$$

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