derivative 3\sqrt[3]{x}

解答

导数

3 3 x

\frac{1}{x ^{\frac{2}{3}}}

求解步骤

\frac{d}{d x} (3 3 x)

将常数提出:

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

= 3 \frac{d}{d x} (3 x)

使用根式运算法则:

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

= 3 \frac{d}{d x} (x^{\frac{1}{3}})

使用幂法则:

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

= 3 \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

化简

3 \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{1}{x ^{\frac{2}{3}}}

= \frac{1}{x ^{\frac{2}{3}}}

\frac{\partial}{\partial x} ((x^{2} + y) e^{3 x + 4 y})

\frac{d y}{d x} = 3 y + y^{4}

\int x 1 + x^{2} d x

\frac{d}{d y} (\frac{x}{x ^{2} + y ^{2}})

x \to 2 lim (4 x - 3)