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:

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.

Example 2

Rule 2 states that the derivative of xⁿ 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 xⁿ 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 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.

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