derivative of (tan(x/2-3)/3)

解

\frac{d}{d x} (\frac{tan ( \frac{x}{2} ) - 3}{3})

\frac{1}{6} sec^{2} (\frac{x}{2})

解答ステップ

\frac{d}{d x} (\frac{tan ( \frac{x}{2} ) - 3}{3})

定数を除去:

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

= \frac{1}{3} \frac{d}{d x} (tan (\frac{x}{2}) - 3)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{3} (\frac{d}{d x} (tan (\frac{x}{2})) - \frac{d}{d x} (3))

\frac{d}{d x} (tan (\frac{x}{2})) = sec^{2} (\frac{x}{2}) \frac{1}{2}

\frac{d}{d x} (3) = 0

= \frac{1}{3} (sec^{2} (\frac{x}{2}) \frac{1}{2} - 0)

簡素化

\frac{1}{3} (sec^{2} (\frac{x}{2}) \frac{1}{2} - 0) : \frac{1}{6} sec^{2} (\frac{x}{2})

= \frac{1}{6} sec^{2} (\frac{x}{2})