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What is the second derivative of f(x)= x^(2/3) (6-x)^(1/3)?
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[QUOTE="Mark44, post: 4574214, member: 147785"] There's a difference between what you [U]think[/U] you wrote and what you [U]actually[/U] wrote. Here's how knowledgeable people would interpret what you wrote: $$f'(x) = 4 - \frac{x}{x^{1/3}}(6 - x)^{2/3}$$ Since you undoubtedly meant for 4 - x to appear in the numerator, you need more parentheses or brackets, in both top and bottom, like so: f'(x) = (4 - x)/[x[SUP]1/3[/SUP](6 - x)[SUP]2/3[/SUP]] Since you need to take the derivative again, it might be easier to leave the derivative as got it the first time; i.e., as a product with negative exponents. It looks nicer by changing the negative exponents to positive exponents, but taking the derivative this time means using the quotient rule. If you leave the first derivative as a product, you can use the product rule, which is a bit simpler than the quotient rule, hence less prone to errors. [/QUOTE]
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What is the second derivative of f(x)= x^(2/3) (6-x)^(1/3)?
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