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3.7 Implicit Differentiation xf(x)f(x)g(x)g(x) f ‘ (x)g ‘ (x) 2821/3 33 33 4422 5
Remember this example… Example If g(x) = x 2 + 2x, evaluate g(x – 3) g( ) = 2 + 2 x x (x -3) g(x-3) = (x 2 – 6x + 9) + 2x - 6 g(x-3) = x 2 – 6x + 9 +
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M3309-F10Week 11.2 FG x + F(x)F(x) G(x)G(x) F(x) + G(x)
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THÉORIE DES GROUPES ET GÉOMÉTRIE · Démonstration.. —Puisque, {(g,x) ∈G×E,g·x= x}= {(g,x),g∈G,x∈Fix(g)}= {(g,x),x∈E,g∈Stab(x)}lesdeuxsommessontégales.Commelesorbitesformentunepartition
1. f( g(x)) = ____ for g(x) = 2x + 1 and f(x) = 4x, if x = 3 2. (f + g)(x) = ____ for g(x) = 3x 2 + 2x and f(x) = 3x + 1 3. (f/g)(x) = ______ for f(x)
Theorem 1 The chain rule If k(x) =f (g(x)), then k’(x) = f ’ ( g(x) ) g’(x)
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This time (f+g)(x)=f(x)+g(x) (f-g)(x)=f(x)-g(x) (fg)(x)=f(x)*g(x) (f/g)(x)=f(x)/g(x), g(x)≠0 (f ∘ g)(x)=f(g(x))
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Find ( f + g )(x f g )(x andFind ( f + g )(x), (f ± g)(x), (x),and x) for each f(x) and g(x). Indicate any restrictions in domain or range. 62/87,21 $16:(5 62/87,21
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Operations on Functions Lesson 2.5 ƒ(g(x)) f(x) + g(x) f(x) - g(x) f(x) ÷ g(x) f(x) ∙ g(x)
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