# How do you differentiate f(x)=(x+1)/sqrtx using the quotient rule?

Apr 6, 2018

$f ' \left(x\right) = \frac{x - 1}{x \sqrt{x}}$

#### Explanation:

Let $f \left(x\right) = \frac{x + 1}{\sqrt{x}}$. To find $f '$, we will use the quotient rule

$\frac{d}{\mathrm{dx}} \frac{u}{v} = \frac{v u ' - u v '}{v} ^ 2$

So

$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \frac{x + 1}{\sqrt{x}} = \frac{\sqrt{x} \frac{d}{\mathrm{dx}} \left(x + 1\right) - \left(x + 1\right) \frac{d}{\mathrm{dx}} \sqrt{x}}{\sqrt{x}} ^ 2 = \frac{\sqrt{x} - \frac{x + 1}{2 \sqrt{x}}}{x} = \frac{2 x - x - 1}{2 x \sqrt{x}} = \frac{x - 1}{2 x \sqrt{x}}$