Find the second derivative of
f(x) = ln [ (3x^3 + 3)^4]
2006-09-27 07:17:12 · 2 answers · asked by Girl 5 in Science & Mathematics ➔ Mathematics
We remember that:
f(x) = ln(x)
(f(x))' = 1/x so
f(x) = y = ln[(3x^3 + 3)^4]
y' = ?
We have: 1/(3x^3 + 3)^4 X 4(3x^3 + 3)^3 X 9x^2
= 4(3x^3 + 3)^3 X 9x^2/(3x^3 +3)^4
= 4(3^3 + 3)^3 X 9x^2/((3x^3 +3)^3.(3x^3 +3)
Answer = 36x^2/(3x^3 + 3)
Nota:'' X '' = multiplication sign.
2006-09-27 07:40:05 · answer #1 · answered by frank 7 · 1⤊ 0⤋
f'(x)=[1/((3x^3 + 3)^4]4((3x^3 + 3)^3) ( 9x^2)
=36 x^2 / (3x^3 + 3)
f''(x)= [ (3x^3 + 3)(72x)-36x^2(9x^2)]/(3x^3 + 3)^2
and then you can try to simplify
2006-09-27 07:19:45 · answer #2 · answered by Anonymous · 1⤊ 0⤋