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3.7 - 3.8 - Derivatives of Inverse Functions

# 3.7 - 3.8 - Derivatives of Inverse Functions - Section 2.6...

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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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