derivative of x^{1/n}

解答

\frac{d}{d x} (x^{\frac{1}{n}})

\frac{x ^{\frac{1 - n}{n}}}{n}

求解步骤

\frac{d}{d x} (x^{\frac{1}{n}})

使用幂法则:

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

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

化简

\frac{1}{n} x^{\frac{1}{n} - 1} : \frac{x ^{\frac{1 - n}{n}}}{n}

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

\frac{\partial}{\partial u} (a u)

\int \frac{x}{e ^{x^{2} - 8}} d x

\frac{\partial}{\partial x} (2 z e^{x yz})

\frac{d}{d θ} (1 - sin (θ))

\int e^{3 x} (1 + e^{3 x})^{7} d x