


The Basic RulesBasic Formulae (the Building Blocks)Most of the functions that we have to deal with are combinations of the following elementary functions:
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 1Rule 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 1Find the derivatives below. Each time you click "New Exercise" a new exercise will be provided.
Example 2Rule 2 states that the derivative of x^{n} is nx^{n}^{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 x^{n} is nx^{n}^{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 x^{1/2}. Exercise 2Find the following derivatives. If the answer contains fractions, do not reduce the fraction. Instead, write all fractions in terms of the original denominator given.  Differentiation Index  The Multiple Rule >> 