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calculus · worked example

Solve 1/x = -1/x^2

Method: قاعدة القوة بأس سالب. 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. أعد كتابته كقوة: 1x=x−1\frac{1}{x} = x^{-1}.

  2. طبّق قاعدة القوة عند n=−1n = -1: ddx(x−1)=(−1)x−2\frac{d}{dx}(x^{-1}) = (-1) x^{-2}.

  3. أعد الكتابة كسرًا: −1x2-\frac{1}{x^2}.

Answer

−1x2-\frac{1}{x^2}

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