Question

Найти производную функции y=-x^2+x+2

Answer 1

y=-x²+x+2
F(x)= -2x+1

Answer 2

Derivative of the Function y = -x^2 + x + 2

To find the derivative of the function y = -x^2 + x + 2, we can use the power rule and the sum rule of differentiation. The power rule states that the derivative of x^n is n*x^(n-1), and the sum rule states that the derivative of the sum of two functions is the sum of their derivatives.

Applying the power rule, we have:

- The derivative of -x^2 is -2x^1, which simplifies to -2x. - The derivative of x is 1. - The derivative of 2 is 0, as it is a constant.

Using the sum rule, we can add the derivatives together:

- The derivative of -x^2 + x + 2 is -2x + 1 + 0.

Therefore, the derivative of the function y = -x^2 + x + 2 is -2x + 1.