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chain_rule - Chain Rule Section 3.5 The derivative of True...

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Chain Rule Section 3.5
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The derivative of x 23 = 23 x 22 True False
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The derivative of x 23 = 23 x 22 True The derivative of (2x+1) 23 = 23 (2x+1) 22 True False
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f(g(x)) = (2x+1) 23 f(x)= x 23 g(x) = 2x+1 The function (2x+1) 23 is a composite function: when you differentiate a composite function, a special rule apply
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Chain Rule
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The derivative of is... tan( x 3 + 2) + 1 + x 3 x + ( x ! sin x ) 100
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f=f(x) g=g(x) f o g(x)= f ( g(x) ) outer function inner function Start from f(x) = cos( x ) +2 Erase x f( ) = cos( )+2 Plug in g(x)=x 2 +1 f(x 2 +1 ) = cos(x 2 +1 )+2 f=cos(x)+2 g=x 2 +1 =f o g(x)
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Given •the (outer) function f(x)= •the (inner) function g(x)= tan(x), find the composition f o g(x): A. f o g(x)= tan( x ) + 1 tan( x ) x + 1 x ! " # $ % & B. f o g(x)= tan x + 1 x ! " # $ % &
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Given find • an (outer) function f(x) • an (inner) function g(x) such that F(x) = f o g(x): F ( x ) = x + 1 x + 1 A . f ( x ) = x + 1 g ( x ) = x + 1 x B . f ( x ) = x + 1 x g ( x ) = x + 1 C . f ( x ) = x g ( x ) = x + 1 x + 1
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Given , find • an (outer) function f(x)
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