> For the complete documentation index, see [llms.txt](https://stephanosterburg.gitbook.io/scrapbook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://stephanosterburg.gitbook.io/scrapbook/math/math-notes/derivative.md).

# derivative

$$f'(x) = lim\_{h->0} \frac{f(x+h)-f(x)}{h}$$ 

$$g'(x) = lim\_{x->t} \frac{g(x)-f(t)}{x-t}$$      same as .    $$g'(x)=lim\_{x->t}\frac{g(t-h)-g(t)}{h}$$

### Slope Forms

1. Point Slope Form: $$y-y\_1 = m(x-x\_1)$$
2. Slope Intercept Form: $$y = mx + b$$
3. Standard Form: $$Ax + By = C$$

***m*** describes the **slope**, ***b*** describes the **y-intercept**

Example: (-3, 6)(6, 0)

$$m => \frac{0-6}{6-(-3)} = -\frac{6}{9} = -\frac{2}{3}$$

1. $$y-6 = -\frac{2}{3}(x+3)$$
2. $$y-6 = -\frac{2}{3}x-2 => y = -\frac{2}{3}x + 4$$
3. $$\frac{2}{3}x + y = 4$$