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Popular >

derivative of (cos(2x)/2)

Solution

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

Solution

- sin (2 x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= \frac{1}{2} (- sin (2 x) \cdot 2)

Simplify

\frac{1}{2} (- sin (2 x) \cdot 2) : - sin (2 x)

= - sin (2 x)

Graph

Popular Examples

integral of sqrt(1+(-(2x)/(1-x^2))^2)

\int 1 + (- \frac{2 x}{1 - x ^{2}})^{2} d x

sum from n=1 to infinity of 1/(9^n)

n = 1 \sum \infty \frac{1}{9 ^{n}}

derivative of sqrt((x-1/(x+1)))

\frac{d}{d x} (\frac{x - 1}{x + 1})

integral from 0 to 1 of |3x-2|

\int_{0}^{1} ∣ 3 x - 2 ∣ d x

limit as x approaches 4 of (|3-x|)/(3-x)

x \to 4 lim (\frac{∣ 3 - x ∣}{3 - x})

Frequently Asked Questions (FAQ)

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