fractional exponent derivative

**av8or91** · December 14th 2009, 02:01 PM

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

**e^(i*pi)** · December 14th 2009, 02:03 PM

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..

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

$\frac{d}{dx}(\sqrt [3]{x} +x) = \frac{1}{3\sqrt [3]{x^2}}+1$

**Prove It** · December 14th 2009, 02:04 PM

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..

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

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

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

$\frac{d^2y}{dx^2} = -\frac{2}{9}x^{-\frac{5}{3}}$ .

**av8or91** · December 14th 2009, 02:09 PM

Thanks, basically trying to find concave up and concave down then the inflection points.

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