Differentiation
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This document provides the definition and an example of using the quotient rule to differentiate a fraction. The quotient rule is defined as the derivative of the denominator times the numerator minus the numerator times the derivative of the denominator, all over the denominator squared. As an example, the derivative of (3x+4)/(x-4) is calculated using the quotient rule and simplifies to (24x-13)/(x-4)^2.
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Differentiation
- 2. QUOTIENT RULE DEFINITION: The quotient rule is defined as the quantity of the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all over the denominator squared. ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? .2 xg xfxgxgxf xg xf dx d ??? ?? ? ? ? ? ?
- 3. EXAMPLE SOLUTION Differentiate. Let and . Then, using the quotient rule x xx 34 24 ?? ? ? 34 24 ??? xxxf ? ? xxg ? ? ? ? ? ? ? 2 2424 24 3434 34 x x dx d xxxx dx d x x xx dx d ??????? ?? ? ? ? ? ? ?? ? ? ? ? 2 243 13484 x xxxxx ?????? ? 2 24 343 x xx ?? ? Now simplify.
- 4. Thank you