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)

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derivative of

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

- 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})

\frac{d}{d t} (\frac{1}{2 \cdot a \cdot t ^{2}})

y = \frac{1}{x ^{2} + x ^{2}}

\frac{2}{x + 10 x + 5}

y = (x^{2} + 3 x)^{4}

(1 + x^{3})^{- 1}

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)