Найти производную функции: 1. y=x^2 (2ln+1) 2. y = (5^sinx+3x) ^6 3. x^2*y+y^2*x+e^y=0

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.

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

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.