 Home > College of Sciences > Institute of Fundamental Sciences > Maths First > Online Maths Help > Calculus > Differentiation > The Basic Rules > Basic Formulae (Building Blocks) SEARCH MASSEY  # The Basic Rules

## Basic Formulae (the Building Blocks)

Most of the functions that we have to deal with are combinations of the following elementary functions:

 f(x) = c, where c is a constant, xn, ln x, ex, sin x and cos x

The derivatives for each of these functions are shown below: The six rules shown above are the building blocks for finding most other derivatives and should be memorized. Rules 3 - 6 are exactly as shown. We will take a brief look now at what is meant by Rules 1 and 2.

### Example 1

Rule 1 states that the derivative of any constant is zero. It does not matter how small or large the constant, whether the constant is a whole number, a fraction or a decimal, or whether it is positive or negative. If the number is a constant, it's derivative is zero. For problems 8. and 9. above, note that π and e are both constants with π ≈ 3.14159. and e ≈ 2.71828.

### Exercise 1

Find the derivatives below. Each time you click "New Exercise" a new exercise will be provided.

 d ( ) = dx

### Example 2

Rule 2 states that the derivative of xn is nxn-1 for any real number n. It does not matter how small or large the constant power is, whether the constant power is a whole number, a fraction or a decimal, or whether it is positive or negative. If n is a real number, the derivative of xn is nxn-1. Pay particular attention to problems 8 and 9 above as you should memorize that the derivative of x is 1 and recall that to find the derivative of the square root of x we first write it as x1/2.

### Exercise 2

Find the following derivatives. If the answer contains fractions, do not reduce the fraction. Instead, write all fractions in terms of the original denominator given.

 d ( ) = dx x x

 Contact Us | About Massey University | Sitemap | Disclaimer | Last updated: November 21, 2012     © Massey University 2003