Question

How would I find the second derivative if f(x)= √(x^3+2) using the quotient rule.

I got to the step where
[(12x√(x^3+2))-(9x^4/√(x^3+2))]/4(x^3+2)

how would i go from that to:
(3x(x^3+8))/(4(x^3+2)^3/2)

Answer 1

y = √(x^3+2)

y' = 3x^2/(2√(x^3+2))

y' =
(6x)(2√(x^3+2)) - (3x^2)(6x^2)/(2√(x^3+2))
-----------------------------------------
4(x^3+2)

24x(x^3+2)-18x^4
------------------------
8(x^3+2)^(3/2)

3x(8(x^3+2)-6x^3)
----------------
8(x^3+2)^(3/2)

3x(8x^3+16-6x^3)
----------------
8(x^3+2)^(3/2)

3x(2x^3+16)
----------------
8(x^3+2)^(3/2)

3x(x^3+8)
----------------
4(x^3+2)^(3/2)