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The differentiation of loge x ,i s1/xdot...

The differentiation of `log_e x ,i s1/xdot` i.e. `d/(dx)((log_e x)=1/x)`

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Let `ln x = log_ex`
We know that `d/dx (logₐ x) = 1 / (x ln a)` Substitute a = e on both sides.
Then we get:
`d/dx (log_e x) = 1 / (x ln e)`
By the properties of natural logarithms, ln e = 1.
So ...
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