Question

use the def. derv. to cal. f'(x) if f(x)=sqrt(2x)

Answer 1

\[\begin{align*}f'(x)&=\lim_{h\to0}\frac{\sqrt{2(x+h)}-\sqrt{2x}}{h}\times\frac{\sqrt{2(x+h)}+\sqrt{2x}}{\sqrt{2(x+h)}+\sqrt{2x}}\\\\
&=\lim_{h\to0}\frac{2(x+h)-2x}{h(\sqrt{2(x+h)}+\sqrt{2x})}
\end{align*}\]