i need to find the derivative of 4/sqrt (x)
Any help?
i'm not sure how you're going about this problem, this is what i'm doing
((4/sqrt(x+h)) - (4/(sqrt(x))) / h then
(4 sqrt (x) - 4sqrt(x +h))/ (h)(x)(x + h) and im not sure where to go from here
i do know simple algebra, i'm not stupid, im just trying to solve this problem the way me teacher is instructing me to
Wow, I had this same exact problem for homework and I don't know how to do it either!!! xD
Using the definition of a derivative method and not the power of the rule, you would then have to find the limit of the right side expression as it approaches h. If you plug in zero for h, you get 0 in the denominator. So what do you do from there since you can't factor?
You can do it like this Power of One
$\displaystyle
\frac{{4\sqrt x - 4\sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}=4\frac{{\sqrt x - \sqrt {x + h} }}{{h\sqrt x \sqrt {x + h} }}\cdot \frac{\sqrt x + \sqrt {x + h}}{\sqrt x + \sqrt {x + h}} =
4\frac{x-(x+h)}{h\sqrt x \sqrt {x + h}}\cdot\frac{1}{\sqrt x + \sqrt {x + h}}=
$
$\displaystyle
4\frac{-h}{h\sqrt x \sqrt {x + h}}\cdot\frac{1}{\sqrt x + \sqrt {x + h}}=
\frac{-4}{(\sqrt x \sqrt {x + h})(\sqrt x + \sqrt {x + h})}
$
Now taking the limit
$\displaystyle
\lim\limits_{h\to0}\frac{-4}{(\sqrt x \sqrt {x + h})(\sqrt x + \sqrt {x + h})}=\frac{-4}{x\cdot2\sqrt{x}}=\frac{-2}{x\sqrt{x}}
$
Hope that helps.
I am sorry if I have ruined this one. He was asking for help and sounded like he was stuck. In hindsight I probarbly should have just posted the first few steps.
I am not a showoff, and am very sorry if I have come across as one.
Should I edit the original post and remove the solution?