Объяснение:
2 В .
1 . а) f '( x ) = ( x⁵ + 6 )' = ( x⁵ )' + 6 ' = 5x⁴ + 0 = 5x⁴ ;
б) g '( x ) = (5x⁻³ - 2x )' = (5x⁻³)' - ( 2x )' = - 15x⁻⁴ - 2 ;
в) t '( x ) = ( 7sinx + 7 )' = 7cosx ;
г) y '( x ) = ( tgx + 1/x )' = 1/cos²x - 1/x² ;
д) f '( x ) = ( 1/x⁴ + 1 )' = ( x⁻⁴ )' + 1 ' = - 4x⁻⁵ + 0 = - 4/x⁵ .
2 . a) f '( x ) = ( x²cosx )' = 2xcosx - x²sinx ;
б) g '( x ) = [ ( x² + 1 )/( x - 2 ) ]' = [ 2x( x - 2 ) - 1*( x² + 1 )]/( x - 2 )² =
= ( 2x² - 4x - x² - 1 )/( x - 2 )² = ( x² - 4x - 1 )/( x - 2 )² ;
в) y '( x ) = ( 8x⁻¹ctgx )' = - 8x⁻²ctgx - 8x⁻¹/sin²x ;
г) m'( x ) = [ ( x - 3 )³/( x + 3 ) ]' = [3( x - 3 )²(x + 3 ) - ( x - 3 )³ *1 ]/( x + 3 )² =
= [ ( x - 3 )²( 3x + 9 - x + 3 )]/( x + 3 )² = [ ( x - 3 )²( 2x + 12 ) ]/( x + 3 )² .
3 . x( t ) = 1/2 t² + 5t - 7 ; v( 3 ) - ? v( t ) = x '( t ) ;
v( t ) = ( 1/2 t² + 5t - 7 )' = t + 5 ; v( t ) = t + 5 ;
v( 3 ) = 3 + 5 = 8 ( м/с ) ; v( 3 ) = 8 м/с .
Объяснение: