need help with derivatives?

Question

Find the first and second derivative of the equations

1) f(x) = x |x + 2|
2) f(x) = 12x^(2/3) - 4x

Answer 1

1) f(x) = x|x+2|

If x < -2:
f'(x) = |x+2| - x
f"(x) = -1 - 1 = -2

If x > -2
f'(x) = |x+2| + x
f"(x) = 1 + 1 = 2

At x = -2, f'(x) is not defined

2) f(x) = 12x^(2/3) - 4x
f'(x) = 12*2/3(x)^(-1/3) - 4
= 8/(x^(1/3)) - 4

f"(x) = -(8/3)/(x^(4/3))

Answer 2

1. f'(x) = abs(2x+1)
f"(x)= 2

2. f'(x) = 8x^(-1/3) - 4
f"(x) = -8/3 x^(-4/3)