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Popular >

derivative of 2cos^2(x/2)

Solution

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

Solution

- sin (x)

Solution steps

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

Take the constant out:

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

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

Simplify

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

= - sin (x)

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\int_{0}^{3} x^{4} + 1 x^{3} d x

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Frequently Asked Questions (FAQ)

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