Question

Find dy/dx by implicit differentiation. tan(x-y)=y/(7+x^(2))

Answer 1

y` = dy/dx
D ( tan ( x - y ) ) = D ( y / (7+x² ) )
(1 - y`) / cos² ( x -y ) = [ y` ( 7 + x² ) - 2 x y ] / ( 7 + x² )²
( 1 - y` ) ( 7 + x² )² = (y` ( 7 + x² ) - 2 xy ) cos² ( x - y )
( 7 + x² )² - y` ( 7 + x² )² = y` ( 7 + x² ) cos²( x - y ) - 2 xy cos² ( x - y )
( 7 + x² )² + 2 xy cos² ( x -y ) = y` ( 7 + x² ) cos²( x - y ) + y²` ( 7 + x² )²
( 7 + x² )² + 2 xy cos² ( x - y ) = y` [( 7 + x² ) cos² ( x - y ) + ( 7 + x² )²]
y ` = [ ( 7 + x² )² + 2 xy cos² ( x - y ) ] / [ (7+x² ) ( cos² ( x - y ) + 7 + x² ) ]