Topic 3.2 - Implicit Differentiation (Circuit) - SOLUTIONS University of Virginia MATH 1310

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Avon High School Name __________________________________ AP Calculus AB Period _____ Score ______ / 10 Skill Builder: Topic 3.2 – Implicit Differentiation (Circuit) Begin in the first cell mark... ed #1 and find the derivative of each given function. To advance in the circuit, search for your answer and mark that cell #2. Continue in this manner until you complete the circuit. Show all pertinent work. 2 2 Find for the circle 25 dy x y dx + = and evaluate dy dx at the point (3, 4 . − ) (3, 4) 2 2 0 2(3) 2( 4) 0 6 3 8 4 dy x y dx dy dx dy dx − + = + − = − = = − Find the slope of the tangent line to the graph of 2 2xy xy y + = when y =1. ( ) 2 2 2 2 2 2 1 1 When 1, 2 (1) (1) 1 3 1 1 2(1) 2 2 (1) 1 3 3 5 2 9 3 3 3 3 2 dy dy dy y x y y x dx dx dx y x x x dy dy dy dx dx dx dy dy dy dy dx dx dx dx  +  +  +  = = + = → =   + + + =     + = → = − → = − 7 2 Find the slope of the tangent line to cos( ) at the point ( 1,1).  x x y = − 6 2 7 6 2 7 sin( ) 7 2 Let 1 and 1 sin( ) 7( 1) (1) ( 1) 2(1) 0 7 2 2 7 7 2 dy x x y x y dx x y dy dx dy dx dy dx dy dx     −  =  +   = − = − − = −  + −  = − = = For the circle centered at the origin with radius 4 and equation 2 2 x y + =16 , find dx dt at the first quadrant point where x = 2 if 3 dy dt = − at that instant. 2 2 0 2(2) 2 12( 3) 0 4 6 12 6 12 6 4 3 12 3 3 3 4 4 4 dx dy x y dt dt dx dt dx dt dx dt  +  =  + − =  = = = = [Show More]

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