Question

What the derivative of lnx?

Answer 1

`1/x`

Explanation:

`y=lnx`

by definition of logarithms

`x=e^y`

differentiate `wrty`

`(dx)/(dy)=e^y`

but

`(dy)/(dx)=1/((dx)/(dy))`

`:.(dy)/(dx)=1/e^y`

`=>(dy)/(dx)=1/x`

Answer 2

`1/x`

Explanation:

By definition, `ln k=int_1^k1/x\ dx` so the derivative is the original `1/x`, because the integral is the "anti-derivative" and vice versa.