If y=lnx, dy/dx=1/x proof

\log _{ e }{ x } =y\\ \\ \therefore \quad x={ e }^{ y }\\ \\ \frac { dx }{ dy } ={ e }^{ y }\\ \\

Now:

\frac { dy }{ dx } =\frac { 1 }{ \frac { dx }{ dy } } \\ \\ \frac { dy }{ dx } =\frac { 1 }{ { e }^{ y } } \\ \\ \frac { dy }{ dx } =\frac { 1 }{ x } \\ \\

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