derivative \sqrt[7]{t}

解答

导数

7 t

\frac{1}{7 t ^{\frac{6}{7}}}

求解步骤

\frac{d}{d t} (7 t)

使用根式运算法则:

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

= \frac{d}{d t} (t^{\frac{1}{7}})

使用幂法则:

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

= \frac{1}{7} t^{\frac{1}{7} - 1}

化简

\frac{1}{7} t^{\frac{1}{7} - 1} : \frac{1}{7 t ^{\frac{6}{7}}}

= \frac{1}{7 t ^{\frac{6}{7}}}

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