1) f(x) = x⁶
f'(x) = 6x⁵
2) y = 2x³ -3x² +1/2 x - 5
y' = 6x² -6x +1/2
3) y = Sin(2x +3)
y' = 2Cos(2x +3)
4) f(x) = x³ +3x² -72x +9 x₀ = 5
f'(x) = 3x² +6x -72
f'(5) = 3*5² +6*5 -72 = 75 +30 -72 = 33
5) f(x) = x²/(x +2) x₀ = - 4
f'(x) = (2x(x +2) - x²*1)/(x +2)² = (2x² +4 -x²)/(x +2)² = (x²+4)/(x +2)²
f'(-4) = (16 +4)/(-4 +2)² = 20/4 = 5