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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\frac{d}{d x} (\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)) : sin^{2} (x)

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

Apply the chain rule:

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

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

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

= 2 sin (x) cos (x)

Use the Double Angle identity:

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

= sin (2 x)

\int \frac{16}{x ^{2} - 4} d x

- 10 x + 11, x^{2} - 5 x - 13

y = \frac{5 x}{( x + 1 ) ^{2}}, (0, 0)

x y^{^{'}} + y^{2} = 0

\int - x d x

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)