How do you use the quotient rule to find the derivative of $y = \frac{x - \sqrt{x}}{x^{\frac{1}{3}}}$ $y=(x-sqrt(x))/(x^(1/3))$ ?

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How do you use the quotient rule to find the derivative of $y = \frac{x - \sqrt{x}}{x^{\frac{1}{3}}}$ $y=(x-sqrt(x))/(x^(1/3))$ ?

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Answer 1 · 2014-09-08T23:42:07

$y'=2/3*1/x^(1/3)-1/6*1/x^(5/6)$

Solution:

$y=(x−sqrtx)/x^(1/3)$

$y=x/x^(1/3)-x^(1/2)/x^(1/3)$

$y=x^(2/3)-x^(1/6)$

differentiating with respect to $x$ ,

$y'=2/3x^(2/3-1)-1/6x^(1/6-1)$

$y'=2/3x^(-1/3)-1/6x^(-5/6)$

$y'=2/3*1/x^(1/3)-1/6*1/x^(5/6)$

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How do you use the quotient rule to find the derivative of $y = \frac{x - \sqrt{x}}{x^{\frac{1}{3}}}$ $y=(x-sqrt(x))/(x^(1/3))$ ?

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How do you use the quotient rule to find the derivative of $y = \frac{x - \sqrt{x}}{x^{\frac{1}{3}}}$ $y=(x-sqrt(x))/(x^(1/3))$ ?