http://i43.tinypic.com/2j11mgy.jpg --> problem is here
I only would like to know how they got that from the derivative equation. Can you please show me step by step how you'd go about doing it, using that formula?
Thanks!!
http://i43.tinypic.com/2j11mgy.jpg --> problem is here
I only would like to know how they got that from the derivative equation. Can you please show me step by step how you'd go about doing it, using that formula?
Thanks!!
They did this:
$\displaystyle \lim_{h\to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt{x}}}{h}$
How, work the algebra magic, take the limit as h approaches 0 and you have it. The derivative of $\displaystyle \frac{1}{\sqrt{x}}$
Note: I used h instead of $\displaystyle {\Delta}x$. Same thing
$\displaystyle
\lim_{h\to 0}\frac{\sqrt{x}-\sqrt{x+h}}{h\sqrt{x+h}\sqrt{x}}$$\displaystyle = \lim_{h\to 0}\frac{\sqrt{x}-\sqrt{x+h}} {h\sqrt{x+h}\sqrt{x}}\cdot \frac{\sqrt{x}+\sqrt{x+h}}{\sqrt{x}+\sqrt{x+h}} $
Expand only the numerator and things in the top will cancel, then cancel the $\displaystyle h$ in the bottom, then take the limit.