must must

Must must - Math 140(07 Homework Set#4 Ae Ja Yee 3.6 Implicit Differentiation Find dy dx by implicit differentiation 14 y sin x 2 = x sin y 2

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 140 (07), Homework Set #4 Ae Ja Yee 3.6 Implicit Differentiation Find dy dx by implicit differentiation. 14. y sin( x 2 ) = x sin( y 2 ) Solution. y sin( x 2 ) + 2 xy cos( x 2 ) = sin( y 2 ) + 2 xyy cos( y 2 ) y (sin( x 2 )- 2 xy cos( y 2 )) = sin( y 2 )- 2 xy cos( x 2 ) y = sin( y 2 )- 2 xy cos( x 2 ) sin( x 2 )- 2 xy cos( y 2 ) 16. √ x + y = 1 + x 2 y 2 Solution. ( x + y ) 1 / 2 = 1 + x 2 y 2 1 2 ( x + y )- 1 / 2 (1 + y ) = 2 xy 2 + 2 x 2 yy y ( 1 2 ( x + y )- 1 / 2- 2 x 2 y ) = 2 xy 2- 1 2 ( x + y )- 1 / 2 y = 2 xy 2- 1 2 ( x + y )- 1 / 2 1 2 ( x + y )- 1 / 2- 2 x 2 y = 4 xy 2 √ x + y- 1 1- 4 x 2 y √ x + y 22. If g ( x ) + x sin g ( x ) = x 2 , find g (0). Solution. g ( x ) + sin g ( x ) + xg ( x )cos g ( x ) = 2 x g ( x )(1 + x cos g ( x )) = 2 x- sin g ( x ) g ( x ) = 2 x- sin g ( x ) 1 + x cos g ( x ) g (0) =- sin g (0) Note that g (0) = 0, so g (0) = 0. 30. Use implicit differentiation to find an equation of the tangent line to the curve at the given point....
View Full Document

This note was uploaded on 07/05/2010 for the course MATH 2240 taught by Professor Crespo during the Spring '09 term at SPSU.

Page1 / 4

Must must - Math 140(07 Homework Set#4 Ae Ja Yee 3.6 Implicit Differentiation Find dy dx by implicit differentiation 14 y sin x 2 = x sin y 2

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online