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The Basic Rules

The Multiple Rule

We now know how to find the derivative of the basic functions: f(x) = c, where c is a constant, xⁿ, ln x, e^x, sin x and cos x. The multiple rule provides us with a rule for finding the derivatives of a constant times any of these basic functions.

Click here to see a proof.

As with the six basic rules, this rule should be memorized. We will take a brief look now at how to use the multiple rule.

Example 3

The multiple rule states that the derivative of any constant times any function is equal to the constant times the derivative of the function. It does not matter what type of function f(x) is or 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.

More

Exercise 3

Find the provided derivatives. Use Excel or MATLAB notation when entering your answers:

<< Basic Formulae (Building Blocks) |  Differentiation Index  |  The Sum and Difference Rules >>