a-maths~~~~~~~

a)x = sin x + tan ( x + y )
1 = cos x + [sec2 ( x + y )]( 1 + dy / dx )
1 = cos x + sec2 ( x + y ) + [sec2 ( x + y )] dy / dx
1 – cos x – sec2 ( x + y ) = [sec2 ( x + y ) ] dy / dx
dy / dx = [1 – cos x – sec2 ( x + y )] / sec2 ( x + y )
b)sin xy = cos ( x² - y² )
(cos xy)[ x ( d / dx ) y + y ( d / dx ) x ] = [- sin ( x² - y² )][d / dx ( x2 ) – d / dx ( y2 )]
( cos xy )[ x ( dy / dx ) + y ] = [- sin ( x² - y² )][ 2x – 2y ( dy / dx )]
x cos xy ( dy / dx ) + y cos xy = [2y sin ( x² - y² )]dy / dx – 2x sin ( x² - y² )
[2y sin ( x² - y² ) – x cos xy] dy / dx = [2x sin ( x² - y² ) + y cos xy]
dy / dx = [2x sin ( x² - y² ) + y cos xy] / [2y sin ( x² - y² ) – x cos xy]