Question

Найти производную f(x)=x^2*(2x-7) с описанием

Answer 1

Ответ на фото............

Answer 2

Calculating the Derivative of f(x) = x^2*(2x-7)

To find the derivative of the function f(x) = x^2*(2x-7), we can use the power rule and the product 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 product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by (u(x)v(x))' = u'(x)v(x) + u(x)v'(x).

Let's apply these rules to find the derivative of f(x) = x^2*(2x-7):

Step 1: Expand the expression inside the parentheses: f(x) = x^2*(2x-7) = 2x^3 - 7x^2

Step 2: Apply the power rule to each term: f'(x) = d/dx(2x^3) - d/dx(7x^2) = 6x^2 - 14x

Therefore, the derivative of f(x) = x^2*(2x-7) is f'(x) = 6x^2 - 14x.

Please let me know if you have any further questions!