Найти производную. y=2x^3-15x^2+36x

Найдем производную функции y (x) = 2x³ - 15x² + 36x, воспользовавшись правилом вычисления производной для степенной функции. Получим:

y' (x) = (2x³ - 15x² + 36x) ' = (2x³) ' - (15x²) ' + (36x) ' = 2 ⋅ (x³) ' - 15 ⋅ (x²) ' + 36 ⋅ (x) ' =

= 2 ⋅ 3 ⋅ x³⁻¹ - 15 ⋅ 2 ⋅ x²⁻¹ + 36 ⋅ 1 ⋅ x¹⁻¹ = 2 ⋅ 3 ⋅ x² - 15 ⋅ 2 ⋅ x¹ + 36 ⋅ 1 ⋅ x⁰ =

= 6 ⋅ x² - 30 ⋅ x + 36 ⋅ 1 = 6x² - 30x + 36.

Ответ: y' = 6x² - 30x + 36.