. Найдите производную функции: а) у=х4; б) у=4 г) у=3х +

а) f(x) = (x * (x 4)) = (x) * (x 4) + x * (x 4) = (x) * (x 4) + x * ((x) (4)) = 1 * (x 4) + x * (1 0) = x 4 + x = 2x 4.

б) f(x)  = (3 2х) = (3) (2х) = 0 2 * 1 * x^{(1 1)} = -2 * x⁰ = -2 * 1 = -2.

г) f(x) = ((-x^2 + 2x^2)^3 + (x - 3)^4) = ((-x^2 + 2x^2)^3) + ((x - 3)^4) = (-x^2 + 2x^2) * ((-x^2 + 2x^2)^3) + (x - 3) * ((x - 3)^4) = ((-x^2) + (2x^2)) * ((-x^2 + 2x^2)^3) + ((x) (3)) * ((x - 3)^4) = (-2x + 4x) * (3 * (-x^2 + 2x^2)^2) + (1 - 0) * (4 * (x - 3)^3) = 2x * 3 * (x^2)^2 + 1 * (4 * (x - 3)^3) = 6x * x^4 + 4(x - 3)^3 = 6x^5 + 4(x - 3)^3.

е) f(x) = (2sin (x)) = 2 * (sin (x)) = 2 * cos (x) = 2cos (x).

з) f(x) = ((3^x) * (x + 1)) = ((3^x) * (x + 1)) + ((3^x) * (x + 1)) = ((3^x) * (x + 1)) + ((3^x) * ((x) + (1)) = (3^x * ln 3) * (x + 1)) + (3^x) * 1 = (3^x * ln 3) * (x + 1)) + (3^x).