There are rules we can follow to find many derivatives.

There are

**rules**we can follow to find many derivatives. For example:- The slope of a
**constant**value (like 3) is always 0 - The slope of a
**line**like 2x is 2, or 3x is 3 etc - and so on.

Here are useful rules to help you work out the derivatives of many functions (with examples below). Note: the little mark ’ means "Derivative of".

Common Functions | Function | Derivative |
---|---|---|

Constant | c | 0 |

Line | x | 1 |

ax | a | |

Square | x^{2} | 2x |

Square Root | √x | (½)x^{-½} |

Exponential | e^{x} | e^{x} |

a^{x} | ln(a) a^{x} | |

Logarithms | ln(x) | 1/x |

log_{a}(x) | 1 / (x ln(a)) | |

Trigonometry (x is in radians) | sin(x) | cos(x) |

cos(x) | −sin(x) | |

tan(x) | sec^{2}(x) | |

Inverse Trigonometry | sin^{-1}(x) | 1/√(1−x^{2}) |

cos^{-1}(x) | −1/√(1−x^{2}) | |

tan^{-1}(x) | 1/(1+x^{2}) | |

Rules | Function | Derivative |

Multiplication by constant | cf | cf’ |

Power Rule | x^{n} | nx^{n−1} |

Sum Rule | f + g | f’ + g’ |

Difference Rule | f - g | f’ − g’ |

Product Rule | fg | f g’ + f’ g |

Quotient Rule | f/g | (f’ g − g’ f )/g^{2} |

Reciprocal Rule | 1/f | −f’/f^{2} |

Chain Rule (as "Composition of Functions") | f Âº g | (f’ Âº g) × g’ |

Chain Rule (using ’ ) | f(g(x)) | f’(g(x))g’(x) |

Chain Rule (using ddx ) | dydx = dydududx |

"The derivative of" is also written ddx

So ddxsin(x) and sin(x)’ are the same thing, just written differently

## Examples

### Power Rule

### Multiplication by constant

### Sum Rule

### Difference Rule

It doesn't have to be

**x**, we can differentiate with respect to, for example,**v**:### Sum, Difference, Constant Multiplication And Power Rules

### Product Rule

### Reciprocal Rule

### Chain Rule

Another way of writing the Chain Rule is: dydx = dydududx

Let's do the previous example again using that formula:

Another couple of examples of the Chain Rule:

## COMMENTS