differentiate

[Ryan$]

hi guys, why in the differentiate we are pointing delta x to be zero .. dx --->0 in the equation of dy/dx ? I'm just wondering about that which if dx=0 then dy/dx is infinity .. so how does that relate to differentiate! ?! any clue?

 

[Ryan$]

I mean with pointing...approaching to..

 

[MarkFL]

We are taking a limit, as the differentials approach zero, but not actually equal to zero:

[MATH]\d{f}{x}\equiv\lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}[/MATH]

 

[Otis]

... why in the differentiate we are pointing delta x to be zero ... dx--->0 in the equation of dy/dx?

It would be nice to see the equation and the material you're looking at (delta x is called dx?), but if you're talking about the derivative definition that MarkFL posted above (limit of a difference quotient) then we let delta x approach zero because we want an instantaneous rate of change and that exists only in the limit.

... if dx=0 then dy/dx is infinity ...

dx never equals zero. (You're not allowed to divide by zero.)

In a limit where a quantity like \(\Delta\)x approaches zero, \(\Delta\)x never reaches zero; it just keeps getting closer.

dy/dx never equals infinity; it always equals a number.

If dy/dx approaches infinity as \(\Delta\)x approaches zero, then the derivative does not exist. When we write dy/dx=infinity, that's an abbreviated way of saying, "the limit does not exist because dy/dx increases without bound".

?