Question

Найти дифференциал функции f(x) = (x^3)*e^x^2

Answer 1

d(f(x)) = d(x^3 × e^(x^2)) = (x^3 × e^(x^2))'× dx = ((x^3)'(e^(x^2)) + (e^(x^2))'x^3)dx = (3x^2 × e^(x^2) + 2x^4 × e^(x^2))dx = (x^2(3e^(x^2) + 2x^2 × e(x^2))dx = e^(x^2) × x^2 × (3 + 2x^2)dx

Ответ : e^(x^2) × x^2 × (3 + 2x^2)dx