Lesson10_-_The_Chain_Rule_ws

Lesson10_-_The_Chain_Rule_ws - f x = xg x 2 ﬁnd f 00 in...

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Worksheet for Section 2.5 The Chain Rule V63.0121, Calculus I Spring 2010 1. Diﬀerentiate each of the following functions. 1. y = ( x 3 - x + 1) 5 2. f ( t ) = 3 1 + tan t 3. y = a 3 + sin 3 x 4. y = sin( a 3 + x 3 ) 1

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2. If r ( x ) = f ( g ( h ( x ))) and h (1) = 2 h 0 (1) = 4 g (2) = 3 g 0 (2) = 5 f 0 (3) = 6 , ﬁnd r 0 (1). 3. If g is a twice diﬀerentiable function and
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Unformatted text preview: f ( x ) = xg ( x 2 ), ﬁnd f 00 in terms of g , g , and g 00 . 4. Show that y = A sin(2 x ) + B cos(2 x ) satisﬁes the diﬀerential equation y 00 + 4 y = 0 . 2...
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Lesson10_-_The_Chain_Rule_ws - f x = xg x 2 ﬁnd f 00 in...

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