y-x-Find-dy-dx-by-first-principle-

Question Number 162675 by Mathematification last updated on 31/Dec/21

y = \sqrt{x}

F i n d \frac{d y}{d x} b y f i r s t p r i n c i p l e .

Answered by tounghoungko last updated on 31/Dec/21

\frac{d y}{d 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{h}{h (\sqrt{x + h} + \sqrt{x})}

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