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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

= 2 \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}

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

Simplify

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

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

\int_{0}^{\frac{π}{4}} cos (x) d x

\frac{d}{d x} (20 x^{- 8} + 5 x^{- 3} - 7 x^{- 7})

\frac{d}{d x} (\frac{1}{x ^{2} - 9 y ^{2}})

\frac{d}{d x} ((1 - x^{2})^{10})

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

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