ID - Contents 2 3 4 5 Differentiation Review Chain Rule...

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Contents 2 Differentiation Review 3 Chain Rule 4 Integration Review 5 u - substitution
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Differentiation Review We’re gonna have two types of problems on the quiz: 1) Draw a curve, and plot points on it, compute velocity vectors, and put ’em with their tails in the right place. 2) Find the length of the curve. In spite of what everyone says about where’s the calculus, I bet no- one is gonnabe all that thrilled about going back to integrating and di±erentiating. So you get a cheat sheet for this one, and there’s some formulae that everyone needs to have: Di±erentiation basic rules: Power Rule :[ x a ] 0 = ax a 1 Special cases : [1] 0 =0 [ x ] 0 =10 [ x 2 ] 0 =2 x [ 1 x ] 0 = 1 x 2 [ x ] 0 = 1 2 x Basic Trig : [sin x ] 0 = cos x [cos x ] 0 = sin x Log and Exponential : [ln x ] 0 = 1 x [ e x ] 0 = e x Product Rule f · g ] 0 =[ f ] 0 · g + f · [ g ] 0 Example : [cos x sin x ] 0 = [cos x ] 0 sin x + cos x [sin x ] 0 sin x ] sin x + cos x [cos x ] = sin 2 x + cos 2 x
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Chain Rule Power Chain Rule :[ f a ] 0 = af a 1 [ f ] 0 Example : [cos 3 x ] 0 = [(cos x ) 3 ] 0 = 3(cos x ) 2 [cos x ] 0 = 3(cos x ) 2 [ sin x ] Example : h p 1 x 2
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This note was uploaded on 03/19/2011 for the course CH 204 taught by Professor Leytner during the Spring '08 term at University of Texas at Austin.

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ID - Contents 2 3 4 5 Differentiation Review Chain Rule...

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