Question

Find the second derivate:

Answer 1

\[f(x)=\sqrt[3]{x^2-1};\]

Answer 2

Well, first you need to find the first derivative, and this will take some use of the chain rule.

Answer 3

I found the first derivate:\[\frac{ 2x }{ 3\sqrt[3]{(x^2-1)^2}}\]

Answer 4

i need someone to explain me the second derivate

Answer 5

To find the second derivative, you just take the derivative of the first derivative according to all the same rules.

Answer 6

i derivate "mot a mot"\[\frac{ 2(3\sqrt[3]{(x^2-1)^2})-2x(\frac{ 4(x^3-x) }{ \sqrt[3]{(x^2-1)^4} }) }{ 3\sqrt[3]{(x^2-1)^2} }\]

Answer 7

but i need a simplified form

Answer 8

well, one thing you can do to simplify it to note that:
\[x^3 -x = x(x^2-1)\]
and that:
\[\sqrt[3]{(x^2-1)^4} = (x^2-1)^{4/3}\]

Answer 9

make \(x^2-1=b\) and \(db=2x\) then
f(x)=\(b^{1/3}\)
f'(x)=\(1/3b^{-2/3}db\)
f''(x)=\(-2/9b^{-5/3}db\)
now just substitute

Answer 10

Because db in f'(x) is technically a function of x, wouldn't you have to derive that as well when finding f''(x) including using the product rule if so?