Proposition: Derivative of the Reciprocal Function

The derivative of the reciprocal function $f(x)=1/x,$ $x\in\mathbb R,$ $x\neq 0$ is $$f'(x)=-\frac{1}{x^2}.$$

The graph of the derivative of the reciprocal function is shown in the following figure:

Proofs: 1


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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983