Find the derivative of y=\cos^{2}(x).

David Troyer

David Troyer

Answered question

2021-12-18

Find the derivative of y=cos2(x).

Answer & Explanation

peterpan7117i

peterpan7117i

Beginner2021-12-19Added 39 answers

y=cos2(x)=(cos(x))2
Thus,
y=2cos(x)×cos(x)=2cos(x)×(sin(x))=2cos(x)×sin(x)=sin(2x)
esfloravaou

esfloravaou

Beginner2021-12-20Added 43 answers

y=cos2(x)=12(1+cos(2x))
y=12×(sin(2x)×(2x))=sin(2x)
RizerMix

RizerMix

Expert2021-12-29Added 656 answers

Apply the chain rule:
2cos(x)ddx(cos(x))
Ans if ddx(cos(x))=sin(x), we substitute:
2cos(x)(sin(x))
Simplify:
2cos(x)(sin(x))=sin(2x)

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