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.