Question

У=х^5-7х^3+3. Найти у^((4)).

Answer 1

Дано: y(x) = x⁵ - 7*x³ + 3

Найти: y""(x) = ?

Пошаговое объяснение:

y' = 5*x⁴ - 21*x²

y" = 20*x³ - 42*x

y'" = 60*x² - 42

y"" = 120 - четвертая производная - ответ.

Answer 2

To find the fourth derivative of the function U(x) = x^5 - 7x^3 + 3, we'll need to take the derivative four times. Each time we take a derivative, the power of x decreases by 1. Here's the step-by-step process:

1. First derivative: U'(x) = d/dx(x^5) - d/dx(7x^3) + d/dx(3) = 5x^4 - 21x^2 + 0 = 5x^4 - 21x^2

2. Second derivative: U''(x) = d/dx(5x^4) - d/dx(21x^2) = 20x^3 - 42x

3. Third derivative: U'''(x) = d/dx(20x^3) - d/dx(42x) = 60x^2 - 42

4. Fourth derivative: U^((4))(x) = d/dx(60x^2) - d/dx(42) = 120x

So, the fourth derivative of U(x) is U^((4))(x) = 120x.