What is the derivative of 2sin(x/2) ?

The derivative of 2sin(x/2) is cos(x/2)

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

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

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

cos (\frac{x}{2})

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int x \cdot cos (4 x) d x

y^{^{'}} = y

\frac{4 - x ^{2}}{x ^{3}}

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

x \to 4 lim (\frac{2 x + 1}{3 x + 3})

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