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 . In this case, we can apply the sum and power rule to find the derivative of the expression.
The formal limit definition of the derivative operator is given below.
The table below shows some common derivatives.
| 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 |