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)

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

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})

y^{^{''}} - y^{^{'}} - 30 y = 0

\frac{16}{s ^{2} + 9}

\frac{\partial}{\partial y} (\frac{4 x}{y})

\frac{d}{d x} (- \frac{1}{2} x^{4})

x \to 4 lim (3 x^{3})

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)