derivative (2x*sqrt(3x-1))/(5x)

解答

导数

\frac{2 x \cdot 3 x - 1}{5 x}

\frac{3}{5 3 x - 1}

求解步骤

\frac{d}{d x} (\frac{2 x 3 x - 1}{5 x})

将常数提出:

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

= \frac{2}{5} \frac{d}{d x} (\frac{x 3 x - 1}{x})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{2}{5} \cdot \frac{\frac{d}{d x} ( x 3 x - 1 ) x - \frac{d x}{d x} x 3 x - 1}{x ^{2}}

\frac{d}{d x} (x 3 x - 1) = \frac{9 x - 2}{2 3 x - 1}

\frac{d x}{d x} = 1

= \frac{2}{5} \cdot \frac{\frac{9 x - 2}{2 3 x - 1} x - 1 \cdot x 3 x - 1}{x ^{2}}

化简

\frac{2}{5} \cdot \frac{\frac{9 x - 2}{2 3 x - 1} x - 1 \cdot x 3 x - 1}{x ^{2}} : \frac{3}{5 3 x - 1}

= \frac{3}{5 3 x - 1}

\int \frac{e ^{x}}{e ^{2 x} + 16} d x

\int \frac{x ^{3}}{9 x ^{2} + 5} d x

\frac{d}{d x} (\frac{x}{∣ x ∣})

\frac{\partial}{\partial x} (π)

- x \frac{d y}{d x} + y = 0