Ответ:
Пошаговое объяснение:
1. f(x) = 3x + 5
f '(x) = 3
2. f(x) = 4x^2 - 5x^3 + 9x
f '(x) = 2*4x - 3*5x^2 + 9 = 8x - 15x^2 + 9
3. f(x) = 3/x + x/3 = 3*x^(-1) + x/3
f '(x) = 3*(-1)*x^(-2) + 1/3 = -3/x^2 + 1/3
4. f(x) = 2/x^2 + 5/x^3 - 7/x = 2x^(-2) + 5x^(-3) - 7x^(-1)
f '(x) = 2*(-2)x^(-3)+ 5*(-3)*x^(-4) - 7*(-1)*x ^(-2) = - 4/x^3 - 15/x^4 + 7/x^2
5. f(x) = √x + 4 = x^(1/2) + 4
f '(x) = (1/2)*x^(1/2-1) = (1/2)*x^(-1/2) = 1/(2*√x)