Thread: Derivative of: ∫1/x dx = ln IxI help...

Could someone show me how to get the derivative of both sides of this equation? I can't quite seem to figure it out. I have an answer, but I'm not sure it is not correct. Thanks for looking.

Here is what I have so far:
y= ln x, so x= e^y
which gives 1= e^y dy/dx
then 1/e^y= dy/dx
which gives 1/e^lnx=dy/dx
and lastly dy/dx= 1/x
Good or not so good?

Differentiating both sides gives .

Why do you need to do this?

part of an assignment that I am stuck on. Could you show me how to go through the steps or no?

Well there aren't really steps to it.

From we know that by the fundamental theorem of calculus.

We also know (from the fundamental theorem of calculus) that

So you can just apply this to both sides of the equation.

Thanks for the help.