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Unformatted text preview: Use the Chain Rule on Power function F ( x ) = [ g ( x )] n ⇒ F ( x ) = n [ g ( x )] n1 · g ( x ) where n is any real number and g ( x ) exists (or g is diﬀerentiable). Example 3 of Section 3.4 (textbook): Example 4 of Section 3.4 (textbook): Example 5 of Section 3.4 (textbook): Example 6 of Section 3.4 (textbook): Use the Chain Rule on Exponential function F ( x ) = e g ( x ) ⇒ F ( x ) = e g ( x ) · g ( x ). What is the derivative of F ( x ) = a x , a > , a 6 = 1 ? F ( x ) = a x = ( e ln a ) x = e (ln a ) x ⇒ F ( x ) = a x ln a . Remarks : In Section 3.1, we learned that if f ( x ) = a x ( a > 0) then f ( x ) = f (0) a x . So, f (0) = ln a . Example 7 of Section 3.4 (textbook): Example 9 of Section 3.4 (textbook):...
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This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.
 Fall '08
 Noohi
 Calculus, Chain Rule, The Chain Rule

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