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Popular >

derivative of 1/2 (1-cos(2x))

Solution

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

Solution

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)

Popular Examples

integral of (16)/(x^2-4)

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

area-10x+11,x^2-5x-13 area

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

tangent of y=(5x)/((x+1)^2),(0,0)tangent of

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

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

integral of sqrt(-x)

\int - x d x

Frequently Asked Questions (FAQ)

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)