# Thread: Final Derivative concern..(some progress)

1. ## Final Derivative concern..(some progress)

the derivative of :

$f(x) = \frac { 6 x^2 + 8 x + 5 } {\sqrt{x} },$

so far i get this using the quotient rule..but it's wrong:

$(12x+8)(x^(-1/2)) + (-1/(2sqrt(x)))(6x^2+8x+5)$

2. here's where i am stuck after using the quotient rule..its showing as incorrect:

[(12x+8x)(sqrt(x)) - [(-1/(2sqrt(x)))(6x^2+8x+5)]]/x

or

$[(12x+8x)(sqrt(x)) - [(-1/(2sqrt(x)))(6x^2+8x+5)]]/x$

3. Originally Posted by frozenflames
the derivative of :

$f(x) = \frac { 6 x^2 + 8 x + 5 } {\sqrt{x} },$

so far i get this using the quotient rule..but it's wrong:

$(12x+8)(x^(-1/2)) + (-1/(2sqrt(x)))(6x^2+8x+5)$
The quotient rule is the hard way and so can lead to mistakes that I'm not even going to bother trying to find.

Break it up as $f(x) = 6 \frac{x^2}{\sqrt{x}} + 8 \frac{x}{\sqrt{x}} + \frac{5}{\sqrt{x}} = 6 x^{3/2} + 8 x^{1/2} + 5 x^{-1/2}$ and differentiate term-by-term.