Calculus 5e_Part105

# Write dy dx y x lim y u u x lim y u lim u x lim 1 lim

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Unformatted text preview: ite dy dx y x lim y u u x lim y u lim u x lim 1 lim y u lim u x xl0 xl0 xl0 ul0 xl0 xl0 (Note that u l 0 as x l 0 since t is continuous.) dy du du dx The only ﬂaw in this reasoning is that in (1) it might happen that u 0 (even when SECTION 3.5 THE CHAIN RULE ❙❙❙❙ 219 x 0) and, of course, we can’t divide by 0. Nonetheless, this reasoning does at least suggest that the Chain Rule is true. A full proof of the Chain Rule is given at the end of this section. The Chain Rule can be written either in the prime notation ftx 2 or, if y f u and u f tx t x t x , in Leibniz notation: dy dx 3 dy du du dx Equation 3 is easy to remember because if dy du and du d x were quotients, then we could cancel du. Remember, however,...
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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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