Why (eˣ)′ = eˣ

About this app

Three-step proof walk: (1) ln′(x) = 1/x from the difference quotient (with e as a limit), (2) inverse function rule — reflection at y=x turns slopes into reciprocals, (3) (eˣ)′ = 1 / (1/eˣ) = eˣ. Live algebra in the proof panel.

Subject: Analysis (one-dimensional)

More from Analysis (one-dimensional)

• Derivative as a sequence of secants
• Bounded growth
• Exponential growth and decay
• Optimisation: the largest rectangle
• Area between curves
• Area function is an antiderivative
• Sequential continuity
• Rational functions and asymptotes

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