x^1/3 + x. I need to find the second derivative. I came up with -2/ 3x^2/3 for the first..(Worried)

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- Dec 14th 2009, 02:01 PMav8or91fractional exponent derivative
x^1/3 + x. I need to find the second derivative. I came up with -2/ 3x^2/3 for the first..(Worried)

- Dec 14th 2009, 02:03 PMe^(i*pi)
- Dec 14th 2009, 02:04 PMProve It
Just use the rule: If $\displaystyle y = ax^n$ then $\displaystyle \frac{dy}{dx} = anx^{n - 1}$.

So $\displaystyle y = x^{\frac{1}{3}} + x$

$\displaystyle \frac{dy}{dx} = \frac{1}{3}x^{-\frac{2}{3}} + 1$

$\displaystyle \frac{d^2y}{dx^2} = -\frac{2}{9}x^{-\frac{5}{3}}$. - Dec 14th 2009, 02:09 PMav8or91
Thanks, basically trying to find concave up and concave down then the inflection points.