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Unformatted text preview: Section 2.6 Derivatives of Inverse
Functions Sections 3.7 and 3.8 The Derivative of an
Inverse Functigrrﬁ Let fbe a function that is differentiable on
an interval I. If fhas an inverse function 9,
then 9 is differentiable at any xfor whidi f T901): 0- MoreOW-‘n QTXF 1/ f T900)- Assinment for next time Section 3.6 Homework ' Section 3.8, ALL of #1~20 WITHOUT
using your calculator AT ALL. [)0 not
even get it out of your bag. Section 3.7 through #40 on the
assignment sheet Derivatives of Inverse Functions 9/23/2009 Continuity & Differentiability
of Inverse Functions“ 21"”???3; uh H 7 Let fbe a function whose domain is an
Interval I. If fhas an inverse, then the
following statements are true. 1. If fis continuous on its domain, then f1
is continuous on its domain. 2. If fis differentiable at cand f '(c): 0,
then f4 is differentiable at f (c). Other Basic Derivatives " Natural Logarithmic Function 1 %[lnx]=; Bases Other than .9 %[a']=<lna)a* 1 d _
a [109“ x} — (In a)x Loarithmic Differentiation Logarithmic differentiation is helpful when we
have a function that oould easily be rewritten
using the basic properties of logarithms. Messy functions Involving radicals and quotients
are good candldalaes. We really a - - logarithmlc differentiation to
differentiate functions where we have a base and
exponent which both involve our variable. Section 2.6 9/23/2009 Steps for Logarithmic
Differentiatlon Thkainofbomsidu Usethe of riﬂimstomwﬂmme ht-
ham Iona do We using impﬂdt dﬂfereumauon.
- Simplify and isolate dy/dx.
Usaﬂ‘eoﬂglnalequaﬂontnmmmteforu ~ Slrnpllfy. Derivatives of Inverse
Trigonometric Evpctip 3“:§2:,..v<-, , £[arcsin x] - dx 1—):2 d —1
Ehrcootx] = mi“ i[arccscx]=— _l -
ab: |xixfx2—1 Derivatives of Inverse Functions ...
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