determine f" if f(x)=sqrt(x^3+2)
f(x)=sqrt(x^3+2)
We can also rewrite this as,
f(x) = (x^3 + 2)^(1/2)
Then we can use chain rule,
f'(x) = (1/2)*(3x^2)*(x^3 + 2)^(-1/2)
Finally, the second derivative is
f''(x) = (3/2)(2x)(x^3 + 2)^(-1/2) + (3/2)(x^2)(3x^2)(-1/2)(x^3 + 2)^(-3/2)
And simplify. Hope this helps~