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Popular >

derivative of 1/2 cos^2(x)

Solution

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

Solution

- cos (x) sin (x)

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \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)

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

Simplify

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

= - cos (x) sin (x)

Graph

Popular Examples

tangent of f(x)= 3/(x^{1/2)}tangent of

f (x) = \frac{3}{x ^{\frac{1}{2}}}

limit as x approaches 3+of (x+2)/(x+3)

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

slope of (-6,-7),(-24,-7)slope

(- 6, - 7), (- 24, - 7)

integral of e^{3x}e^{-5x}

\int e^{3 x} e^{- 5 x} d x

(\partial)/(\partial x)((x-y)/(30-y))

\frac{\partial}{\partial x} (\frac{x - y}{30 - y})

Frequently Asked Questions (FAQ)

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