Question

1.1 Найдите производные функции у = х3+х2-1

Answer 1

Решение производной функции:

Answer 2

у³ = (x^3+x^2-1)³ = 3x^2+2x

³ -этот знак я использовала вместо штриха

Answer 3

Derivative of the Function u(x) = x^3 + x^2 - 1

To find the derivative of the function u(x) = x^3 + x^2 - 1, we can use the power rule of differentiation. According to the power rule, the derivative of x^n, where n is a constant, is given by n*x^(n-1).

Applying the power rule to each term in the function u(x), we get:

u'(x) = d/dx (x^3) + d/dx (x^2) - d/dx (1)

The derivative of x^3 is 3x^(3-1) = 3x^2.

The derivative of x^2 is 2x^(2-1) = 2x.

The derivative of a constant is zero, so the derivative of -1 is 0.

Therefore, the derivative of the function u(x) = x^3 + x^2 - 1 is:

u'(x) = 3x^2 + 2x - 0

Simplifying, we have:

u'(x) = 3x^2 + 2x.

This is the derivative of the given function u(x) = x^3 + x^2 - 1