Lecture 3_2

Lecture 3_2 - d dx ( f ( x ) g ( x ) ) = g ( x ) f ( x ) -f...

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Lecture 3.2 The Product and Quotient Rules I. Product Rule: p. 194 in text d dx ( f g ) = df dx g ( x ) + dg dx f ( x ) = f g + g f You differentiate one function at a time! The first thing to notice is that the derivative of a product is NOT simply the product of the derivatives. Look at an example that you easily multiply out before differentiating so we can check the product rule works. Example: h ( x ) = x 2 (3 x + 4) a) First, ignore the new rule and multiply the polynomials out and then use the differentiation rules from the last section. b) Second, use the product rule to find the derivative of h(x) II. Quotient Rule:
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Unformatted text preview: d dx ( f ( x ) g ( x ) ) = g ( x ) f ( x ) -f ( x ) g ( x ) [ g ( x )] 2 = lowdhigh-highdlow lowsquared the second expression that I typed is a cute way to memorize the quotient rule it seems to stick Again lets work and example that we can divide out first to avoid the new rule and then use the new rule to verify it is correct. Example j ( x ) = x 4- 3 x 2 x a) First, divide j(x) and then differentiate b) Second, use the quotient rule and simplify until we see the methods result in the same function. Further examples:...
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Lecture 3_2 - d dx ( f ( x ) g ( x ) ) = g ( x ) f ( x ) -f...

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