Essential Differentiation Formulas for Basic Functions in Calculus
This section provides key differentiation formulas for basic functions, essential for understanding calculus. Learn the derivative of constant functions, identity functions, and the power rule for integer exponents. Explore rules such as the constant multiple rule, addition and subtraction rules for differentiable functions, multiplication and quotient rules, and a mnemonic to remember the quotient rule. These foundational concepts are critical for solving calculus problems and are summarized effectively for easy reference.
Essential Differentiation Formulas for Basic Functions in Calculus
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Presentation Transcript
Section 3.3 Differentiation Formulas
DIFFERENTIATION FORMULAS FOR BASIC FUNCTIONS 1. The derivative of a constant function, f (x) = c 2. The derivative of the identity function, f (x) = x
THE POWER RULE Let n be any integer other than zero. Then the derivative of the function f (x) = xn is
THE CONSTANT MULTIPLE RULE If c is a constant and f is a differentiable function, then
THE ADDITION AND SUBTRACTION RULES If f and g are both differentiable functions, then
THE MULTIPLICATION RULE If f and g are both differentiable functions, then Another way to write this is
THE QUOTIENT RULE If f and g are differentiable, then Another way to write this is
A MNEMONIC DEVICE FOR THE QUOTIENT RULE If the function in the numerator is called “hi” and the function in the denominator is called “ho,” the quotient rule can be remembered with the following mnemonic phrase. ho D hi minus hi D ho over ho ho In mathematical notation, this would be ho D hi − hi D ho ho ho Recall that “D” means “derivative of.”
All the derivative rules are summarized in the box on page 154 of the text.
