(\partial)/(\partial x)(x^{1/4})

解答

\frac{\partial}{\partial x} (x^{\frac{1}{4}})

\frac{1}{4 x ^{\frac{3}{4}}}

求解步骤

\frac{\partial}{\partial x} (x^{\frac{1}{4}})

使用幂法则:

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

= \frac{1}{4} x^{\frac{1}{4} - 1}

化简

\frac{1}{4} x^{\frac{1}{4} - 1} : \frac{1}{4 x ^{\frac{3}{4}}}

= \frac{1}{4 x ^{\frac{3}{4}}}

x \to 1 lim (2 x + 3)

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