How Can I Improve My Understanding of Differentiating Equations?

[fluidistic]

My friend came up with the following:
$2x=1 \Rightarrow \frac{d}{dx}(2x)=\frac{d}{dx}1 \Rightarrow 2=0$. Shamefully I do not see what's wrong with this reasoning!
Can someone help me? :)

 

[LCKurtz]

2x=1 is not an identity. It is only true for x = 1/2.

 

[fluidistic]

Thank you LcKurtz, that makes sense.