What is the derivative of 1/2 cos(x/2) ?

The derivative of 1/2 cos(x/2) is -1/4 sin(x/2)

What is the first derivative of 1/2 cos(x/2) ?

The first derivative of 1/2 cos(x/2) is -1/4 sin(x/2)

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

- \frac{1}{4} sin (\frac{x}{2})

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

Simplify

\frac{1}{2} (- sin (\frac{x}{2}) \frac{1}{2}) : - \frac{1}{4} sin (\frac{x}{2})

= - \frac{1}{4} sin (\frac{x}{2})

What is the derivative of 1/2 cos(x/2) ?
The derivative of 1/2 cos(x/2) is -1/4 sin(x/2)
What is the first derivative of 1/2 cos(x/2) ?
The first derivative of 1/2 cos(x/2) is -1/4 sin(x/2)