What is the derivative of-1/8 cos(x/2) ?

The derivative of-1/8 cos(x/2) is 1/16 sin(x/2)

What is the first derivative of-1/8 cos(x/2) ?

The first derivative of-1/8 cos(x/2) is 1/16 sin(x/2)

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\frac{d}{d x} (- \frac{1}{8} cos (\frac{x}{2}))

\frac{1}{16} sin (\frac{x}{2})

Solution steps

\frac{d}{d x} (- \frac{1}{8} cos (\frac{x}{2}))

Take the constant out:

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

= - \frac{1}{8} \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}{8} (- sin (\frac{x}{2}) \frac{1}{2})

Simplify

- \frac{1}{8} (- sin (\frac{x}{2}) \frac{1}{2}) : \frac{1}{16} sin (\frac{x}{2})

= \frac{1}{16} sin (\frac{x}{2})

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What is the derivative of-1/8 cos(x/2) ?
The derivative of-1/8 cos(x/2) is 1/16 sin(x/2)
What is the first derivative of-1/8 cos(x/2) ?
The first derivative of-1/8 cos(x/2) is 1/16 sin(x/2)