derivative of 2tan(x+pi/(12))

解答

\frac{d}{d x} (2 tan (x + \frac{π}{12}))

2 sec^{2} (x + \frac{π}{12})

求解步骤

\frac{d}{d x} (2 tan (x + \frac{π}{12}))

将常数提出:

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

= 2 \frac{d}{d x} (tan (x + \frac{π}{12}))

使用连锁律:

sec^{2} (x + \frac{π}{12}) \frac{d}{d x} (x + \frac{π}{12})

= sec^{2} (x + \frac{π}{12}) \frac{d}{d x} (x + \frac{π}{12})

\frac{d}{d x} (x + \frac{π}{12}) = 1

= 2 sec^{2} (x + \frac{π}{12}) \cdot 1

化简

= 2 sec^{2} (x + \frac{π}{12})

\frac{d}{d x} ((x + 1)^{\frac{2}{3}} (3 x^{2} - 2)^{3})

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