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DIFFERENTIATION RULES

3. DIFFERENTIATION RULES. DIFFERENTIATION RULES. The functions that we have met so far can be described by expressing one variable explicitly in terms of another variable. For example, , or y = x sin x , or in general y = f ( x ). DIFFERENTIATION RULES.

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DERIVATIVES

3. DERIVATIVES. DERIVATIVES. The functions that we have met so far can be described by expressing one variable explicitly in terms of another variable. For example, , or y = x sin x , or in general y = f ( x ). DERIVATIVES.

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DERIVATIVES

3. DERIVATIVES. DERIVATIVES. 3.6 Implicit Differentiation. In this section, we will learn: How functions are defined implicitly. DERIVATIVES. The functions that we have met so far can be described by expressing one variable explicitly in terms of another variable.

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DERIVATIVES

3. DERIVATIVES. DERIVATIVES. The functions that we have met so far can be described by expressing one variable explicitly in terms of another variable. For example, , or y = x sin x , or in general y = f ( x ). DERIVATIVES.

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5-Minute Check 1

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EXAMPLE 4

STEP 1. Write the prime factorization of each expression. 12 a 3 = 2 2 3 a a a. 9 a 2 = 3 3 a a. EXAMPLE 4. Finding the GCF of Monomials. Find the greatest common factor of 12 a 3 and 9 a 2. STEP 2. Find the common factors, 3 and a 2 . The GCF is their product. ANSWER.

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EXAMPLE 4

STEP 1. Write the prime factorization of each expression. 12 a 3 = 2 2 3 a a a. 9 a 2 = 3 3 a a. EXAMPLE 4. Finding the GCF of Monomials. Find the greatest common factor of 12 a 3 and 9 a 2. STEP 2. Find the common factors, 3 and a 2 . The GCF is their product. ANSWER.

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