Пошаговое объяснение:
a) y'=-12x³-4=-4*(3x³-1).
б) y=3*x⁴*⁵√x⁴=3*x⁴*x⁴/⁵=3*x⁽⁴⁺⁽⁴/⁵⁾⁾=3*x*⁽²⁴/⁵⁾.
y'=3*(24/5)*x⁽¹⁹/⁵⁾=(72/5)*x⁽¹⁹/⁵⁾.
в) y'=((9x³-8)/sinx)'=((9x³-8)'*sinx-(9x³-8)*(sinx)')/sin²x=
=(27x²*sinx-(9x³-8)*cosx)/sin²x.
г) y'=51*(3*x⁵⁴-6x²)'/(3*x⁵⁴-6*x²)=51*(162*x⁵³-12x)/(3*(x⁵⁴-2*x²)=
51*6*(27*x⁵³-2*x²)/(3*(x⁵⁴-2*x²)=102*x*(27*x⁵²-2)/(x²*(x⁵²-2))=
=102*(27x⁵²-2)/(x*(x⁵²-2)).
д) y'=(√(x³+1))'+(cos²(5x))'=(x³+1)'/(2*√(x³+1))+5*2*cos(5x)*(cos(5x))'=
=3x²/(2*√(x³+1)-5*2*cos(5x)*sin(5x)=3x²/(2*√(x³+1)-5*sin(10x).
Пошаговое объяснение:
a) y'=-12x³-4=-4*(3x³-1).
б) y=3*x⁴*⁵√x⁴=3*x⁴*x⁴/⁵=3*x⁽⁴⁺⁽⁴/⁵⁾⁾=3*x*⁽²⁴/⁵⁾.
y'=3*(24/5)*x⁽¹⁹/⁵⁾=(72/5)*x⁽¹⁹/⁵⁾.
в) y'=((9x³-8)/sinx)'=((9x³-8)'*sinx-(9x³-8)*(sinx)')/sin²x=
=(27x²*sinx-(9x³-8)*cosx)/sin²x.
г) y'=51*(3*x⁵⁴-6x²)'/(3*x⁵⁴-6*x²)=51*(162*x⁵³-12x)/(3*(x⁵⁴-2*x²)=
51*6*(27*x⁵³-2*x²)/(3*(x⁵⁴-2*x²)=102*x*(27*x⁵²-2)/(x²*(x⁵²-2))=
=102*(27x⁵²-2)/(x*(x⁵²-2)).
д) y'=(√(x³+1))'+(cos²(5x))'=(x³+1)'/(2*√(x³+1))+5*2*cos(5x)*(cos(5x))'=
=3x²/(2*√(x³+1)-5*2*cos(5x)*sin(5x)=3x²/(2*√(x³+1)-5*sin(10x).