Differentiate the following function

$\displaystyle \frac{5x^2+7x+6}{\sqrt{x}}$

= $\displaystyle \frac{10x+7+0}{x^\frac{1}{2}} $

= $\displaystyle (x^\frac{-1}{2})(10x+7)$

= $\displaystyle 10x^\frac{1}{2}+7x^\frac{-1}{2}$

where am i going wrong?

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- Sep 29th 2008, 01:24 PMsilencecloakDerivative with short cut
Differentiate the following function

$\displaystyle \frac{5x^2+7x+6}{\sqrt{x}}$

= $\displaystyle \frac{10x+7+0}{x^\frac{1}{2}} $

= $\displaystyle (x^\frac{-1}{2})(10x+7)$

= $\displaystyle 10x^\frac{1}{2}+7x^\frac{-1}{2}$

where am i going wrong? - Sep 29th 2008, 01:27 PMThePerfectHacker
$\displaystyle \frac{5x^2 + 7x + 6}{x^{1/2}} = 5x^{3/2} + 7x^{1/2} + 6x^{-1/2}$

Now take the derivative.

You__cannot__just take the derivative of numerator and leave the denominator. And you__cannot__just take the derivative of numerator and denominator at the same time. You need to use the quotient rule, if you learned that. But the best is that do what I did.

This is Mine 1:)7:):)th Post!!! - Sep 29th 2008, 01:37 PMsilencecloak
so i end up with

$\displaystyle

\frac{15}{2}x^\frac{1}{2} + \frac{7}{2}x^\frac{-1}{2}-\frac{6}{2}x^\frac{-3}{2}$ - Sep 29th 2008, 01:45 PMsilencecloak
still wrong :/

- Sep 29th 2008, 02:11 PMskeeter
- Sep 29th 2008, 02:12 PMsilencecloak