# Thread: Derivative with short cut

1. ## 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?

2. 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 17th Post!!!

3. 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}$

4. still wrong :/

5. Originally Posted by silencecloak
still wrong :/
no, it's correct ... maybe some simplification is necessary.

6. 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