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MTH132-Quiz3-Solutions (1)

# MTH132-Quiz3-Solutions (1) - Page 1 Name(Print Clearly...

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Page 1 10/18/2011 Name (Print Clearly): Student Number: MTH132 Section 5 & 18, Quiz 3 Oct 3, 2008 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 15 minutes. 1 [3 pts each] . Find dx dy / for following functions (Do Not Simplify) (a) 3 2 x y = (Ex 3.6 #3) 3 / 1 ) 2 ( x y = (use the rational power rule) So 3 / 2 3 / 2 ) 2 ( 3 2 ) 2 ( ) 2 ( 3 1 ' - - = = x x dx d x y (b) x x y 2 2 sin sin + = 2 2 ) (sin ) sin( x x y + = (use the Chain rule) So x x x x x dx d x x dx d x y cos sin 2 ) 2 ( ) cos( ) (sin sin 2 ) ( ) cos( ' 2 2 2 + = + = (c) x x y 5 cos 5 4 3 sin 3 4 π π + = (Ex 3.5 #21) - = - + = ) 5 sin( 4 ) 3 cos( 4 ) 5 ( ) 5 sin ( 5 4 ) 3 ( ) 3 cos( 3 4 ' x x x dx d x x dx d x y π π π π (d) 6 2 2 = + xy y x (use implicit differentiation) (Ex 3.6 #19) consider y as a function of x (implicitly) apply dx d to this implicit equation: 0 ) 6 ( ' 2 ' 2 2 2 = = + + + dx d y y x y y x xy so xy x xy y y xy y y xy x 2 2 ' ) 2 ( ' ) 2 ( 2 2 2 2 + + - = + - = +

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