Derivative of sqrt(x) from 1st principles (1 Viewer)

Drongoski · May 19, 2012

Per request from StormieNormie

$\frac {d \sqrt x}{dx} = \lim_{h \to 0} \frac {\sqrt {x+h} - \sqrt x}{h} = \lim_ {h \to 0} \frac {\sqrt {x+h}-\sqrt x}{h} \times \frac {\sqrt{x+h}+\sqrt x}{\sqrt {x+h}+\sqrt x}$

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

$= \frac {1}{2\sqrt x}$

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Derivative of sqrt(x) from 1st principles (1 Viewer)

Drongoski

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