derivative of 4cos(x/2)

解答

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

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

求解步骤

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

将常数提出:

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

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

使用连锁律:

- 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})

化简

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

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