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Popular Calculus >

derivative of 4cos(x/2)

Solution

\frac{d}{d x} (4 cos (\frac{x}{2}))

Solution

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

Solution steps

\frac{d}{d x} (4 cos (\frac{x}{2}))

Take the constant out:

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

= 4 \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}

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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