# Derivative with short cut

• September 29th 2008, 01:24 PM
silencecloak
Derivative with short cut
Differentiate the following function

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

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

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

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

where am i going wrong?
• September 29th 2008, 01:27 PM
ThePerfectHacker
Quote:

Originally Posted by silencecloak
Differentiate the following function

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

$\frac{5x^2 + 7x + 6}{x^{1/2}} = 5x^{3/2} + 7x^{1/2} + 6x^{-1/2}$
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!!!
• September 29th 2008, 01:37 PM
silencecloak
so i end up with

$

\frac{15}{2}x^\frac{1}{2} + \frac{7}{2}x^\frac{-1}{2}-\frac{6}{2}x^\frac{-3}{2}$
• September 29th 2008, 01:45 PM
silencecloak
still wrong :/
• September 29th 2008, 02:11 PM
skeeter
Quote:

Originally Posted by silencecloak
still wrong :/

no, it's correct ... maybe some simplification is necessary.
• September 29th 2008, 02:12 PM
silencecloak
Quote:

Originally Posted by skeeter
no, it's correct ... maybe some simplification is necessary.

well

this online math homework stuff :(

i even simplified the fractions to decimals