AI Math
開啟應用程式
calculus · worked example

Solve 1/x = -1/x^2

Method: 帶負指數的冪法則. Verified step-by-step solution with our free AI math solver.
Problem

ddx(1x)\frac{d}{dx}\bigl(\tfrac{1}{x}\bigr)

Step-by-step solution

  1. 改寫成冪的形式：1x=x−1\frac{1}{x} = x^{-1}。

  2. 以 n=−1n = -1 套用冪法則：ddx(x−1)=(−1)x−2\frac{d}{dx}(x^{-1}) = (-1) x^{-2}。

  3. 再寫回分數形式：−1x2-\frac{1}{x^2}。

Answer

−1x2-\frac{1}{x^2}

Want to solve a different problem? Open the derivative solver →

Related worked examples