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

1. ## 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?

2. $\displaystyle \int \frac{1}{x}~dx= \ln x$

Differentiating both sides gives $\displaystyle \frac{1}{x}=\frac{1}{x}$.

Why do you need to do this?

3. ## it is...

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

4. Well there aren't really steps to it.

From $\displaystyle \int \frac{1}{x}~dx= \ln x$ we know that $\displaystyle \frac{d}{dx} \ln x =\frac{1}{x}$ by the fundamental theorem of calculus.

We also know (from the fundamental theorem of calculus) that $\displaystyle \frac{d}{dx}\int \frac{1}{x}~dx= \frac{1}{x}$

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

5. ## thanks!

Thanks for the help.