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

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

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

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

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derivative of

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

- sin (2 x)

Solution steps

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

Simplify

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

x \to - 1 lim (2 e^{x - 1})

\int 3 x - 1 d x

5 x, x^{2} - 6, - 6, 0

0.01 x^{2} - 3 x + 229, 429 - 2 x, x = 0

\frac{\partial}{\partial x} (8 e^{x y} + 5)

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