Найдите производную функции: а) f(x)= -2\3 x^3+2x^2-x б) f(x)= -1\3 x^3+4x^2+2x в) g(x)= 4\x^2+x г) g(x)=4ctgx, вычислить

а ) f ( x ) = - 2 / 3 * x ^ 3 + 2 * x ^ 2 - x ; f \' ( x ) = ( - 2 / 3 * x ^ 3 + 2 * x ^ 2 - x ) \' = - 2 / 3 * 3 * x ^ ( 3 - 1) + 2 * 2 * x ^ ( 2 - 1 ) - 1 = - 2 * x ^ 2 + 4 * x - 1 ; б ) f ( x ) = - 1 / 3 * x ^ 3 + 4 * x ^ 2 + 2 * x ; f \' ( x ) = ( - 1 / 3 * x ^ 3 + 4 * x ^ 2 + 2 * x ) \' = - 1 / 3 * 3 * x ^ 2 + 4 * 2 * x + 2 * 1 =- x ^ 2 + 8 * x + 2; в ) g ( x ) = 4 / x ^ 2 + x ; g \' ( x ) = 4 * ( - 2 ) * 1 / x ^ 3 + 1 = - 8 / x ^ 3 + 1 ; г ) g ( x ) = 4 * ctgx ; g \' ( - 2 п / 3 ) = 4 * ( - 1 / sin ^ x ) = - 4 / sin ^ 2 x = - 4 / sin ^ 2 ( - 2 * pi / 3 ) = 4 * √ 3 / 2 = 2 √ 3; д ) h ( x ) = 3 + 2 * x / ( x - 2 ) ; h \' ( 1 ) = 2 * ( x - 2 - x ) / ( x - 2 ) ^ 2 = - 4 / ( x - 2 ) ^ 2 = - 4 / ( 1 - 2 ) ^ 2 = - 4 / 1 = - 4 ;е ) h ( x ) = ( 3 * x + 4 ) / ( x - 3 ) ; h \' ( 4 ) = ( 3 * ( x - 3 ) - ( 3 * x + 4 ) ) / ( x - 3 ) ^ 2 = ( 3 * x - 9 - 3 * x - 4 ) / ( x - 3) ^ 2 = - 13 / ( x - 3 ) ^ 2 = - 13 / ( 4 - 3 ) ^ 2 = - 13 / 1 = - 13.