Is d/dxf(x) the Same as f'(x) for Finding Derivatives?

[Jarfi]

ahhh guys, is d/dxf(x)=f'(x)?

I just don't get it, my classmates are finding the deravative of f(x), i'd think that d/dx(f(x))=f'(f(x))=some annoying long equations...

but they get d/dx(f(x))=f'(x)? am I doing a silly mistake here?

 

[Mark44]

I just don't get it, my classmates are finding the deravative of f(x), i'd think that d/dx(f(x))=f'(f(x))=some annoying long equations...

Your classmates are right. Your mistake seems to be in thinking that d/dx is the same as f'. It's not. d/dx is an operator that works on a function; f' already is a function.

$\frac{df(x)}{dx}$ and f'(x) are essentially two different notations for the same thing.

but they get d/dx(f(x))=f'(x)? am I doing a silly mistake here?

 

[Jarfi]

Your classmates are right. Your mistake seems to be in thinking that d/dx is the same as f'. It's not. d/dx is an operator that works on a function; f' already is a function.

$\frac{df(x)}{dx}$ and f'(x) are essentially two different notations for the same thing.

damn I'm stupid... well thanks a LOT. It's 1 am but who needs sleep! go homework&euroshopper energy drink