Why d/dx (lnx) = 1/x? Here's the proof.
This video shows the proof of the derivative of ln x by using the first principle.

Proof of the derivative of log x 👉 [ Ссылка ]
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Proof of the derivative of e^x by using the first principle and followed by two different approaches at [ Ссылка ]

Proof of the limit of (1+1/n)^n = e using:
1. L’Hopital’s rule at [ Ссылка ]
2. Binomial theorem at [ Ссылка ]

Proof of the derivative of ln x using:
1. the Chain rule at [ Ссылка ]
2. the first principle at [ Ссылка ]

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If have to prove more than one case at once. Here are some combinations.

limit of (1+1/n)^n = e and d/dx(lnx) = x
- Proof of the derivative of e^x (graphical approach) at [ Ссылка ]
- Proof of the derivative of ln x (chain rule) at [ Ссылка ]
- Proof of (1+1/n)^n = e (L’Hopital’s rule) at [ Ссылка ]
or
- Proof of (1+1/n)^n = e (binomial theorem) at [ Ссылка ]
- Proof of the derivative of ln x (first principle) at [ Ссылка ]

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