The derivative is one of the main operators in calculus. The derivative of a function with a respect to returns a function that represents the change in over the change in . For example, the derivative operator typically appears in an expression like this:

In plain language, this means take the derivative of the function with respect to the variable .

The formal limit definition of the derivative operator is given below.

The table below shows some common derivatives for polynomial, trigonometric and exponential functions. The coefficients , and are highlighted blue to make them distinct from the variables of the functions.

Function | Derivative |
---|---|

Constant | |

Line | |

Quadratic | |

Cubic | |

Polynomial | |

Sine | |

Cosine | |

Exponential | |

Logarithm |

Shown below are some common rules when taking the derivatives of more complex functions.

Name | Rule |
---|---|

Sum Rule | |

Product Rule | |

Power Rule | |

Chain Rule |