What is the derivative of (1+cos(2x)/2) ?

The derivative of (1+cos(2x)/2) is -sin(2x)

What is the first derivative of (1+cos(2x)/2) ?

The first derivative of (1+cos(2x)/2) is -sin(2x)

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\frac{d}{d x} (\frac{1 + cos ( 2 x )}{2})

- sin (2 x)

Solution steps

\frac{d}{d x} (\frac{1 + cos ( 2 x )}{2})

Simplify

\frac{1 + cos ( 2 x )}{2} : cos^{2} (x)

= \frac{d}{d x} (cos^{2} (x))

Apply the chain rule:

2 cos (x) \frac{d}{d x} (cos (x))

= 2 cos (x) \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

= 2 cos (x) (- sin (x))

Simplify

2 cos (x) (- sin (x)) : - sin (2 x)

= - sin (2 x)

What is the derivative of (1+cos(2x)/2) ?
The derivative of (1+cos(2x)/2) is -sin(2x)
What is the first derivative of (1+cos(2x)/2) ?
The first derivative of (1+cos(2x)/2) is -sin(2x)