# Thread: alternative form of a derivative?

1. ## alternative form of a derivative?

the definition of a derivative is to find the slope of a tangent line.....
the alternate form of the derivative is for???

2. Originally Posted by maybnxtseasn
the definition of a derivative is to find the slope of a tangent line.....
the alternate form of the derivative is for???
the slope of a tangent line at a specific point.

3. $\lim_{x\to c}=\frac{f(x)-f(c)}{x-c}$ is the alternate form of a derivative.

While $\lim_{\Delta x\to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}$ is the definition of derivative.

The alternate form will give you the value of the derivative at x=c

So really the definition of a derivative ${f}'(x)$ really maps all of the alternate definitions of a derivative at all x values in the domain of f(x)