first principle help!!

**crystal91** · January 18th 2010, 11:36 AM

k

**skeeter** · January 18th 2010, 12:13 PM

$f(x+h) = \sqrt{2(x+h)}<br />$

$f(x) = \sqrt{2x}$

$\frac{\sqrt{2(x+h)} - \sqrt{2x}}{h} \cdot \frac{\sqrt{2(x+h)}+ \sqrt{2x}}{\sqrt{2(x+h)}+ \sqrt{2x}}$

$\frac{2(x+h) - (2x)}{h\left[\sqrt{2(x+h)}+ \sqrt{2x}\right]}$

$\frac{2h}{h\left[\sqrt{2(x+h)}+ \sqrt{2x}\right]}$

$\frac{2}{\sqrt{2(x+h)}+ \sqrt{2x}}$

$\lim_{h \to 0} \frac{2}{\sqrt{2(x+h)}+ \sqrt{2x}} = \frac{2}{2\sqrt{2x}} = \frac{1}{\sqrt{2x}}$

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