Question

Знайти похідну функції у=( 2х^4-х)^5 До вечора . Будь ласка повна відповідь.

Answer 1

Ответ:

Объяснение:

Это сложная функция, производная сложной функции по формуле

(f(g(x)))'=f'(g)g'(x)

сначала белем производную степенной функции по формуле (xⁿ)'=nxⁿ⁻¹ затем умножаем ее на производную  2х⁴-х

у'=(( 2х⁴-х)⁵)'=5( 2х⁴-х)⁴( 2х⁴-х)'=5( 2х⁴-х)⁴(8х³-1)

Answer 2

Finding the Derivative of the Function

To find the derivative of the function u = (2x^4 - x)^5, we can use the power rule and the chain rule of differentiation.

The power rule states that if we have a function of the form f(x) = x^n, then its derivative is given by f'(x) = nx^(n-1).

The chain rule states that if we have a composite function of the form f(g(x)), then its derivative is given by f'(g(x)) * g'(x), where f'(g(x)) is the derivative of the outer function and g'(x) is the derivative of the inner function.

Let's apply these rules to find the derivative of the given function.

The function u = (2x^4 - x)^5 can be rewritten as u = (2x^4 - x) * (2x^4 - x) * (2x^4 - x) * (2x^4 - x) * (2x^4 - x).

Using the chain rule, we can find the derivative of each term (2x^4 - x) and multiply them together.

The derivative of (2x^4 - x) with respect to x is (8x^3 - 1).

Therefore, the derivative of the function u = (2x^4 - x)^5 is:

u' = 5 * (2x^4 - x)^4 * (8x^3 - 1).

Let me know if there's anything else I can help with!