d/(dt)(1/(12sqrt(t)))

解答

\frac{d}{d t} (\frac{1}{12 t})

- \frac{1}{24 t ^{\frac{3}{2}}}

求解步骤

\frac{d}{d t} (\frac{1}{12 t})

将常数提出:

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

= \frac{1}{12} \frac{d}{d t} (\frac{1}{t})

使用指数法则:

\frac{1}{a} = a^{- 1}

= \frac{1}{12} \frac{d}{d t} (t^{- \frac{1}{2}})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{12} (- \frac{1}{2} t^{- \frac{1}{2} - 1})

化简

\frac{1}{12} (- \frac{1}{2} t^{- \frac{1}{2} - 1}) : - \frac{1}{24 t ^{\frac{3}{2}}}

= - \frac{1}{24 t ^{\frac{3}{2}}}

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