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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})

Simplify

\frac{- cos ( 2 x )}{2} : - \frac{cos ( 2 x )}{2}

= \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)

Popular Examples

limit as x approaches-1+of 3/(x^2-1)

x \to - 1 + lim (\frac{3}{x ^{2} - 1})

integral from 0 to 1 of x(e^{-x^2})

\int_{0}^{1} x (e^{- x^{2}}) d x

(\partial)/(\partial z)(x^{y^z})

\frac{\partial}{\partial z} (x^{y^{z}})

y^'=(-4y+44)^{1/2}

y^{^{'}} = (- 4 y + 44)^{\frac{1}{2}}

y^'-5y=(cos(x))*e^{5x}

y^{^{'}} - 5 y = (cos (x)) \cdot e^{5 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)