Remember however that du has not been dened and du d

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Unformatted text preview: that du has not been defined and du d x should not be thought of as an actual quotient. sx 2 EXAMPLE 1 Find F x if F x 1. SOLUTION 1 (using Equation 2): At the beginning of this section we expressed F as Fx f tx f t x where f u fu we have 1 2 u 1 2 su 12 Fx x2 su and t x and 1. Since tx 2x f tx t x 1 2 sx 2 1 x2 S OLUTION 2 (using Equation 3): If we let u dy du du dx Fx 1 2 sx 2 x 2x sx 2 1 and y 1 su, then 1 2x 2 su 1 2x x sx 2 1 When using Formula 3 we should bear in mind that dy d x refers to the derivative of y when y is considered as a function of x (called the derivative of y with respect to x), whereas dy du refers to the derivative of y when considered as a function of u (the derivative of y with respect to u). For instance, in Example 1, y can be considered as a...
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This note was uploaded on 12/27/2013 for the course MATHEMATIC 135 taught by Professor Lam during the Fall '07 term at University of Toronto- Toronto.

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