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$f(x)=x^{\frac{1}{3}}$ where $x=27$
i did it in this way
=$3\sqrt{27}$
=3

but the answer is ${\frac{1}{27}}$
this chapter name is (differentiationg rational power $x^{\frac{p}{q}}$)
Can you please help me to solve this question?
thanks in advance

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    Explain more *what*? You should be taking the derivative at some point (first, as it turns out). You never took the derivative. So that's a problem.2012-04-03

1 Answers 1

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First find f'(x). This is important, find the general form of the derivative first:

Using the power rule $ {d\over dx} x^a=ax^{a-1}, $ we have,

f'(x)= {d\over dx}x^{1/3}={\textstyle{1\over3}}x^{{1\over3}-1}={\textstyle{1\over3}} x^{-2/3}={{1\over 3 x^{2/3}}}.

So, whatever $x$ is (as long as it isn't zero), f'(x)={{1\over 3 x^{2/3}}}. Now you know the rule for the function f'(x), and you can evaluate f'(27).

Can you take it from here? (Note $27^{2/3}=(27^{1/3})^2$. )

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    hehe..thx! understood now!2012-04-03