Differential Calculus studies the rates at which quantities change, I.e. continuous change, or rate of change of a function. it focuses on obtaining the solution to the problems where the rate of a function changes or different properties of integrals and derivatives of functions should be determined.

Concepts:

- Limit:
, and , here is called the limit to the function , which can be written as - Interval: An interval defines as the range of numbers that are existing between the two given numbers.

- Open interval: represent all possible complete real numbers in a particular set represented as where .

- Closed interval: represent all possible complete real numbers in a particular set represented as where .

- Half Closed Interval: - Domain: The domain of a function is the input values of a function.
- Range: The range of a function is the output value of a function.

The derivatives of the function determine the rate of change of a function at a point, it is also called the slope of a function and therefore also defined as the ratio of the change in the value of a dependent variable to the change in the independent variable. The procedure used to obtain the derivatives is called differentiation.

in function

Derivative gives us the slope at the point x. Meaning that it describes how a small change in the input x will affect output y.

If

**partial derivative** is used in functions with multiple input.

- The Constant Rule
- The Power Rule
- Multiplied by a Constant Rule
- Sum Rule
- Difference Rule
- Product Rule
- Quotient Rule
- Sum/Difference involving a Constant Rule

Function | Differentiation Formula |
---|---|

C (Constant Function) | |

Square Function | |

Exponential Functions | |

Log Functions | |

Trigonometric Functions | |

Inverse Trigonometric Functions |

Interactive Graph