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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
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$\frac{1}{3}\left(\frac{x\left(x-6\right)}{x^2+2}\right)^{-\frac{2}{3}}\frac{d}{dx}\left(\frac{x\left(x-6\right)}{x^2+2}\right)$
Learn how to solve problems step by step online. Find the derivative of y=((x(x-6))/(x^2+2))^1/3. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Since the exponent is negative, we can invert the fraction. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. The power of a product is equal to the product of it's factors raised to the same power.