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 equation and differentiate it to find its derivative equation (f prime of x).

Differentiation with constants (in sums)

For equation where equation is a constant, equation.

Example: equation.

Differentiation with constants (in products with terms of x)

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

Example: equation.

Differentiation with powers of x

For equation, equation.

Example 1: equation.
Example 2: equation.
Example 3: equation

Differentiation of sums

For equation, equation.

Example: equation.

Differentiation of differences

For equation, equation.

Example: equation.

Differentiation of products

For equation, equation.

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

Differentiation of quotients

For equation, equation.

Example: equation

Trigonometric functions

f(x) f’(x)
equation equation
equation equation
equation equation
equation equation
equation equation
equation equation

Example: equation.

Exponential and logarithmic functions

For equation, equation.

For equation, equation.

For equation, equation.

For equation, equation

Chain rule

For equation, equation.

Example 1: equation.
Example 2: equation.