Precalculus Examples

$\frac{\frac{1}{\sqrt{x + h}} - \frac{1}{\sqrt{x}}}{h}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + h}$ as ${(x + h)}^{\frac{1}{2}}$ .

$\frac{\frac{1}{{(x + h)}^{\frac{1}{2}}} - \frac{1}{\sqrt{x}}}{h}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\frac{\frac{1}{{(x + h)}^{\frac{1}{2}}} - \frac{1}{x^{\frac{1}{2}}}}{h}$