Найдите производную функции:а)y=x^2*e^x б)y=ln(5x^2+9) Найдите точки экстремума функции:y=6x^2-x^3

f(x)\' = (2x^4 – x^2 + 1)’ = (2x^4)’ – (x^2)’ + (1)’ = 2 * 4 * x^(4 – 1) – 2 * x^(2 - 1) – 0 =

8 * x^3 – 2 * x^1 = 8x^3 – 2x.

f(x)\' = ((1 / 2) * x^2 – (1 / 5) * x^5)’ = ((1 / 2) * x^2)’ – ((1 / 5) * x^5)’ = (1 / 2) * 2 * x^(2 - 1) – (1 / 5) * 5 * x^(5 - 1) = 1 * x^1 – 1 * x^4 = x – x^4.

f(x)\' = (x^2 - 3x + 1)’ = (x^2)’ – (3x)’ + (1)’ = 2 * x^(2 – 1) – 3 * x^(1 - 1) – 0 = 2x – 3.

f(x)\' = (3 – 2x + 4x^2 – 7x^3)’ = (3)’ – (2x)’ + (4x^2)’ – (7x^3)’ = 0 – 2 * x^(1 – 1) + 4 * 2 * x^(2 - 1) – 7 * 3 * x^(3 – 1) = -2 * x^0 + 8 * x^1 – 21 * x^2 = -2 + 8x – 21x^2.

f(x)\' = (x^5 + x^3 – x^2 – 1)’ = (x^5)’ + (x^3)’ – (x^2)’ – (1)’ = 5 * x^(5 – 1) + 3 * x^(3 – 1) – 2 * x^(2 – 1) – 0 = 5x^4 + 3x^2 – 2x.