derivative of 2e^{cos(x/2})

解答

\frac{d}{d x} (2 e^{c o s (\frac{x}{2})})

- e^{c o s (\frac{x}{2})} sin (\frac{x}{2})

求解步骤

\frac{d}{d x} (2 e^{c o s (\frac{x}{2})})

将常数提出:

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

= 2 \frac{d}{d x} (e^{c o s (\frac{x}{2})})

使用连锁律:

e^{c o s (\frac{x}{2})} \frac{d}{d x} (cos (\frac{x}{2}))

= e^{c o s (\frac{x}{2})} \frac{d}{d x} (cos (\frac{x}{2}))

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

= 2 e^{c o s (\frac{x}{2})} (- sin (\frac{x}{2}) \frac{1}{2})

化简

2 e^{c o s (\frac{x}{2})} (- sin (\frac{x}{2}) \frac{1}{2}) : - e^{c o s (\frac{x}{2})} sin (\frac{x}{2})

= - e^{c o s (\frac{x}{2})} sin (\frac{x}{2})

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