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: .