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

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

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

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

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

cos (\frac{x}{2})

Solution steps

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

Simplify

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

= \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 - 2 x d x

y = e^{x^{2} + 9 x + 4}

y = 3 x^{2}, y = 16 - x^{2}

\int \frac{2}{5 x 9 - 49 x ^{2}} d x

\frac{d x}{d t} = sin (2 t) - 3 x

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