Do we need to differentiate ‘e’ when d/dx[ e ln x]

e is a constant (≈ 2.71828183) so no.

But isn’t it inside the bracket? And if I differentiate a constant(e) it will become zero right ?

We can also consider the product rule where differentiating e ln x will give us

e d/dx ln x PLUS ln x times d/dx e

First term is e/x
Second term after the plus is ln x times 0, which is the differentiating constant numbers thing.

Constants can always be taken out.

Eg. Lets say y = 2x

dy/dx = d/dx (2x) = 2

But we can also say

dy/dx = d/dx (2x)

= 2 d/dx (x)

= 2 (1)

= 2

The result is the same.

To verify that the constant can be taken out :

Use product rule like Eric mentioned.


① d/dx ( e lnx)

= e (d/dx (lnx)) + (d/dx (e)) lnx

= e (1/x) + (0)lnx

= e (1/x) + 0

= e/x


② d/dx (e lnx)

= e (d/dx (lnx))

= e (1/x)

= e/x


We get the same result for ① and ②

Perhaps the e is confusing you. Just note that it's a constant.


Eg. Let's say I replace e with 2.718,

d/dx (2.718 lnx)

= 2.71(1/x)
= 2.71/x


Likewise,


if I replace e with another constant like π,

Then d/dx (π lnx)

= π (1/x)

= π/x

Once we know the constant can be taken out, we can save all the trouble of differentiating it via product rule