How do find the derivative of y=cos^2(x)?

omreknaqec7

omreknaqec7

Answered question

2023-02-15

How do find the derivative of y = cos 2 ( x ) ?

Answer & Explanation

Gustavo Gamble

Gustavo Gamble

Beginner2023-02-16Added 3 answers

Step 1
First of all y = cos 2 x = ( cos x ) 2
Thus,
y = 2 cos x ( cos x ) = 2 cos x ( - sin x ) = - 2 cos x sin x = - sin 2 x
Step 2
Another way is
y = cos 2 x = 1 2 ( 1 + cos 2 x )
Therefore,
y = 1 2 ( - sin 2 x ( 2 x ) ) = - sin 2 x

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