differential equation

trigonometric derivative

example

Derivada Frigontoo Y = senx ( 3 * ) Of = y = senx 6( 3*3) + 3x((senx) dx y' = senx ( 9* ) + 3*) ( cosx ) Y" = 9 x2 senx + 3* cos xy ' = cosx ( 3/ 8 * 5 ) y' = cos x ( 3 * 5 ) simplify d 3 x cos ( x ) dx 8 3 . d Apply product rule [ vcx). " ( x (Eucx ). vex) + u ( x ). " (x ) 8 dx ( x5 Cos ( x ) ] Apply power rule = 3 ( 2x [ X ] . COS ( x ) + *5. [coscx ) ] ) Apply differentiation rule. [ cos ( x ) ] = - sin ( x ) 8 = 3 ( 5 X " cos* + x 5 . ( - sin(*) ] simplify 8 3 ( 5 X 4 cos( x ) + x 5 sin ( x ) 8 Answer : 15 x cos (x ) - 3 x sin (x ) 3 x4 . (x sin (x) - 5 cos (x ) ) or 8 8 text. fxsingly -ExigonmTea 2 day 7 , t cy = 7 XY + 3cost BY = Senx ( 34X 3 ) @ XX day # 8tang *+ cost @ Y = Cost + 2 @ y = Cotyx sent cost