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**Unformatted text preview: **Lecture 13 1 Lecture 13: (Sec. 3.3) The Chain Rule Rules of Differentiation: A Summary Let f and g be differentiable functions of x : 1) Simple Power Rule : If f ( x ) = x n , then f ( x ) = 2) Product Rule : d dx [ f ( x ) g ( x )] = 3) Quotient Rule : d dx [ f ( x ) g ( x ) ] = Lecture 13 2 ex. Find f ( x ) if f ( x ) = ( x + 1) 2 √ x . Lecture 13 3 Find the equation of the tangent line to f ( x ) = ( x + 1) 2 √ x at x = 1. Lecture 13 4 ex. Let f ( x ) = x 50 . Then f ( x ) = But if h ( x ) = ( x 3- 2 x +1) 50 , how do we find h ( x )? NOTE: h ( x ) is the composite of two simpler functions Lecture 13 5 To Differentiate a Composite Function ex. Find f ( x ) for f ( x ) = ( x 3- 2 x + 1) 2 . Rule 7: The Chain Rule Let f and g be differentiable functions of x and let h ( x ) = f ( g ( x )). Then h ( x ) is a differentiable func- tion of x and h ( x ) = Lecture 13 6 Equivalently, if y = f ( u ) is a differentiable function of u and u = g ( x ) is a differentiable function of x , then...

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