## What is differentiation?

Differentiation is used to find the derivative of a function. We show the different rules that apply when differentiating. We are given a function and differentiate it to find its derivative (f prime of x).

### Differentiation with constants (in sums)

For where is a constant, .

Example: .

### Differentiation with constants (in products with terms of x)

For where is some other function of , . We need to differentiate in this case but unlike a constant in a sum, the constant here which is part of the product with does not disappear.

Example: .

### Differentiation with powers of x

For , .

Example 1: .

Example 2: .

Example 3:

### Differentiation of sums

For , .

Example: .

### Differentiation of differences

For , .

Example: .

### Differentiation of products

For , .

Example: (the differential of is as explained later).

### Differentiation of quotients

For , .

Example:

### Trigonometric functions

f(x) | f’(x) |
---|---|

Example: .

### Exponential and logarithmic functions

For , .

For , .

For , .

For ,

## Chain rule

For , .

Example 1: .

Example 2: .