а) f ( x ) = ( 4 - 3 * x ) * 100 ; Производная f ( x ) = ( ( 4 - 3 * x ) * 100 ) \' = 100 * ( 4 - 3 * x ) \' = 100 * ( 4 \' - ( 3 * x ) \' ) = 100 * ( 0 - 3 * x \' ) = 100 * ( 0 - 3 * 1 ) = 100 * ( - 3 ) = - 100 * 3 = - 300 ; б) y ( x ) = √ ( x ^ 4 + 1 ) ; Производная y ( x ) = ( √ ( x ^ 4 + 1 ) ) \' = 1 / √ ( x ^ 4 + 1 ) * ( x ^ 4 + 1 ) \' = 1 / √ ( x ^ 4 + 1 ) * 4 * x ^ 3 = 4 * x ^ 3 / √ ( x ^ 4 + 1 ); в) f (x) = sin2x-cos3x ; Производная y ( x ) = ( sin2x-cos3x ) \' = cos x * 2 - ( - sin x ) * 3 = 2 * cos x + 3 * sin x ; г) y (x) = sin^2x ; Производная y ( x ) = ( sin^2x ) \' = 2 * sin x * cos x = sin ( 2 * x ).