Производна

[Гост]

y = [tex]6x^{2} . ln^{3} (sin2x)[/tex]

[Knowledge Greedy]

[tex]y'=6.(x^2)'.ln^3(sin2x)+6x^2(ln^3(sin2x))'[/tex]

[tex]y'=12x.ln^3(sin2x)+6x^2.3ln^2(sin2x)\frac{1}{sin2x}(sin2x)'[/tex]

[tex]y'=12x.ln^3(sin2x)+18x^2.ln^2(sin2x)\frac{1}{sin2x}cos2x(2x)'[/tex]

[tex]y'=12x.ln^3(sin2x)+36x^2.3ln^2(sin2x)cotg2x[/tex]

Отговор. [tex]y'=12x.ln^3(sin2x)+36x^2.cotg2xln^2(sin2x)[/tex]