Derivative of x² Notation: \frac{{df(x)}}{{dx}}

[danago]

Hey. Just a quick simple question. If i have a function such as:
$$y = x^2$$

Id write the derivative of function y with respect to x as:
$$\frac{{dy}}{{dx}} = 2x$$

What if the function of x was given as:
$$f(x) = x^2$$

I know i could write the derivative as f'(x), but how would i write it in the form i used for the first function. Would this be what i should write:
$$\frac{{df(x)}}{{dx}}$$
?

Would i write:
$$\frac{{df}}{{dx}}$$
?

Does it even matter? Thanks for the quick advice

Dan.

 

[TD]

Both are used: the first one emphasizes the fact that f is a function of x, the second is of course shorter, which is desirable as well sometimes.

 

[danago]

ok thanks :)

 

[3trQN]

i would write the f(x) on its own following the d/dx fraction, but its just a matter of personal preference to me.

 

[danago]

i would write the f(x) on its own following the d/dx fraction, but its just a matter of personal preference to me.

Like this?
$$\frac{d}{{dx}}(x^2 ) = 2x$$

 

[TD]

Yes, this expression is particularly handy when the expression becomes larger.

 

[danago]

ok thanks again :)

 

[FrogPad]

Another short hand is:
$$y = x^2$$
$$y_x = 2x$$
The $$\frac{dy}{dx}$$ notation is called Leibniz notation. Check out http://en.wikipedia.org/wiki/Leibniz_notation

 

[danago]

Oo thanks frog. I had never really seen that last [itex]y_x[/tex] notation.[/itex]