> For the complete documentation index, see [llms.txt](https://solomons-mathbook.gitbook.io/calculus-basics/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://solomons-mathbook.gitbook.io/calculus-basics/comment-389389887/comment-390102382.md).

# Basic Differential Rules

![image](https://user-images.githubusercontent.com/14041622/40227636-a305cc52-5ac1-11e8-9fbe-ac7e11dd4a6f.png)

> [`Jump over to Basic Integral Rules`](https://github.com/solomonxie/solomonxie.github.io/issues/49#issuecomment-395356656)

[▼Refer to Math is fun: Derivative Rules](https://www.mathsisfun.com/calculus/derivatives-rules.html)

| Rules              | Function                                                                                                       | Derivative                                                                                                     |
| ------------------ | -------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------- |
| Constant           | c                                                                                                              | 0                                                                                                              |
| With constant      | c·f                                                                                                            | c·f’                                                                                                           |
| Power Rule         | xⁿ                                                                                                             | n·xⁿ⁻¹                                                                                                         |
| Sum Rule           | f + g                                                                                                          | f’ + g’                                                                                                        |
| Difference Rule    | f - g                                                                                                          | f’ − g’                                                                                                        |
| Product Rule       | f · g                                                                                                          | fg’ + f’ g                                                                                                     |
| Quotient Rule      | f / g                                                                                                          | (f’g − g’f ) / g²                                                                                              |
| Reciprocal Rule    | 1 / f                                                                                                          | −f’ / f²                                                                                                       |
| Chain Rule         | f(g(x))                                                                                                        | f’(g(x)) · g’(x)                                                                                               |
| Exponent Rule      | eˣ                                                                                                             | eˣ                                                                                                             |
| aˣ                 | aˣ · ln(a)                                                                                                     |                                                                                                                |
| Log Rule           | ![image](https://user-images.githubusercontent.com/14041622/46215573-508d6f80-c370-11e8-8d23-3a56fa227323.png) | ![image](https://user-images.githubusercontent.com/14041622/46215576-53886000-c370-11e8-939a-be092755d1a3.png) |
| Natural Log Rule   | ln(x)                                                                                                          | 1/x                                                                                                            |
| Exponential Rule   | ![image](https://user-images.githubusercontent.com/14041622/46215472-06a48980-c370-11e8-84df-75e1ef944283.png) | ![image](https://user-images.githubusercontent.com/14041622/46215448-f8ef0400-c36f-11e8-9cd3-ec629802a91c.png) |
| Trig Rules         | sin(x)                                                                                                         | cos(x)                                                                                                         |
| cos(x)             | −sin(x)                                                                                                        |                                                                                                                |
| tan(x)             | sec²(x) = 1/cos²(x)                                                                                            |                                                                                                                |
| sec(x)             | sec(x)·tan(x)                                                                                                  |                                                                                                                |
| csc(x)             | -csc(x)·cot(x)                                                                                                 |                                                                                                                |
| cot(x)             | −csc²(x) = -1/sin²(x) = -(1+cot²(x))                                                                           |                                                                                                                |
| Inverse Trig Rules | arcsin(x)                                                                                                      | 1/√(1−x²)                                                                                                      |
| arccos(x)          | −1/√(1−x²)                                                                                                     |                                                                                                                |
| arctan(x)          | 1/(1+x²)                                                                                                       |                                                                                                                |

[▼Refer to Wiki: Differentiation rules](https://en.wikipedia.org/wiki/Differentiation_rules) ![image](https://user-images.githubusercontent.com/14041622/42408397-9fbb09ae-81fe-11e8-8a2e-d7ba9f89dbf3.png)