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Popular >

derivative of cos^2(x/2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

y^{''}-2y^'-3y=e^{-t}

y^{^{''}} - 2 y^{^{'}} - 3 y = e^{- t}

derivative of (e^{2x}-e^x+1/(e^x))

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

integral from 0 to 1 of 11xsqrt(x^2+36)

\int_{0}^{1} 11 x x^{2} + 36 d x

xy^'+2y^'-(x+2)sin(x)+y=0

x y^{^{'}} + 2 y^{^{'}} - (x + 2) sin (x) + y = 0

(\partial)/(\partial x)((x^2y-y^3)^5)

\frac{\partial}{\partial x} ((x^{2} y - y^{3})^{5})

Frequently Asked Questions (FAQ)

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