# fractional exponent derivative

• Dec 14th 2009, 02:01 PM
av8or91
fractional 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 PM
e^(i*pi)
Quote:

Originally Posted by av8or91
x^1/3 + x. I need to find the second derivative. I came up with -2/ 3x^2/3 for the first..(Worried)

For differentiation multiply by the exponent before taking one from said exponent

$\frac{d}{dx}(\sqrt [3]{x} +x) = \frac{1}{3\sqrt [3]{x^2}}+1$
• Dec 14th 2009, 02:04 PM
Prove It
Quote:

Originally Posted by av8or91
x^1/3 + x. I need to find the second derivative. I came up with -2/ 3x^2/3 for the first..(Worried)

Just use the rule: If $y = ax^n$ then $\frac{dy}{dx} = anx^{n - 1}$.

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

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

$\frac{d^2y}{dx^2} = -\frac{2}{9}x^{-\frac{5}{3}}$.
• Dec 14th 2009, 02:09 PM
av8or91
Thanks, basically trying to find concave up and concave down then the inflection points.