I am having some difficulty finding the derivative of this equation:

http://i49.tinypic.com/35jdoxt.png

Can anyone assist me in solving this?

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- Feb 2nd 2013, 08:24 PMmichellederzFinding the Derivative of the Given Function
I am having some difficulty finding the derivative of this equation:

http://i49.tinypic.com/35jdoxt.png

Can anyone assist me in solving this? - Feb 2nd 2013, 08:56 PMProve ItRe: Finding the Derivative of the Given Function
First, I would rewrite the function as $\displaystyle \displaystyle \begin{align*} g(x) = \sqrt{10} \, \sqrt{x} \end{align*}$ and remember that the derivative of a function times a constant is equal to that constant times the derivative. So really, you just need to find the derivative of $\displaystyle \displaystyle \begin{align*} \sqrt{x} \end{align*}$.

$\displaystyle \displaystyle \begin{align*} f(x) &= \sqrt{x} \\ \\ f(x + h) &= \sqrt{x + h} \\ \\ f'(x) &= \lim_{h \to 0}\frac{f(x+ h) - f(x)}{h} \\ &= \lim_{h \to 0}\frac{\sqrt{x + h} - \sqrt{x}}{h} \\ &= \lim_{h \to 0}\frac{\left( \sqrt{x + h} - \sqrt{x} \right) \left( \sqrt{x + h} + \sqrt{x} \right) }{h \left( \sqrt{x + h} + \sqrt{x} \right) } \\ &= \lim_{h \to 0}\frac{ x + h - x }{h \left( \sqrt{x + h} + \sqrt{x} \right) } \\ &= \lim_{h \to 0}\frac{h}{h \left( \sqrt{x + h} + \sqrt{x} \right) } \\ &= \lim_{h \to 0}\frac{1}{\sqrt{x + h} + \sqrt{x}} \\ &= \frac{1}{\sqrt{x + 0} + \sqrt{x}} \\ &= \frac{1}{\sqrt{x} + \sqrt{x}} \\ &= \frac{1}{2\sqrt{x}} \end{align*}$

Therefore if $\displaystyle \displaystyle \begin{align*} g(x) = \sqrt{10} \, \sqrt{x} \end{align*}$ then $\displaystyle \displaystyle \begin{align*} g'(x) = \frac{\sqrt{10}}{2\sqrt{x}} \end{align*}$. - Feb 2nd 2013, 09:02 PMmichellederzRe: Finding the Derivative of the Given Function
Thanks so much!

- Feb 2nd 2013, 09:04 PMProve ItRe: Finding the Derivative of the Given Function
- Feb 2nd 2013, 09:05 PMmichellederzRe: Finding the Derivative of the Given Function
I figured it out. My math book just had it in a different form for whatever reason..

It put the answer as:

5/(square root of 10x)