derivative of sqrt((1-x/x))

解答

\frac{d}{d x} (\frac{1 - x}{x})

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

求解步骤

\frac{d}{d x} (\frac{1 - x}{x})

使用连锁律:

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

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

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

= \frac{1}{2 \frac{1 - x}{x}} (- \frac{1}{x ^{2}})

化简

\frac{1}{2 \frac{1 - x}{x}} (- \frac{1}{x ^{2}}) : - \frac{1}{2 x ^{\frac{3}{2}} - x + 1}

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

d er i v a t i v e y = sin (tan (4) x^{5})

\int \frac{1}{x ^{2} - 2 x + 101} d x

\int sec^{5} (4 x) d x

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

\frac{\partial}{\partial x} (y^{6} cos (4 x) \cdot 4)