derivative of sqrt(1/x)

解答

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

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

x \to 1 + lim (\frac{x ^{2}}{∣ 1 - x ∣})

\int_{0}^{π} cos (θ) d θ

\frac{d}{d a} (a^{5} + a^{2} b^{3} - a^{3} b^{2} - b^{5})

\int \frac{2}{5} x^{\frac{5}{2}} d x

\frac{d x}{d t} = 4 x - x^{3}