Struggling to understand derivative – math.stackexchange.com

I was looking at this solution for $\displaystyle \frac{d}{dx} \frac1x$ $$\require{cancel}\frac d{dx}\frac1x=\frac dd\frac1{x^2}=\frac{\cancel d}{\cancel d}\frac1{x^2}=-\frac1{x^2}$$ I guess it makes ...

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