This preview shows page 1. Sign up to view the full content.
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
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
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...
View Full Document