# How do you find the derivative of sqrt(x+7)?

$\frac{d}{\mathrm{dx}} \sqrt{x + 7} = \frac{1}{2 \sqrt{x + 7}}$

#### Explanation:

Solution:

The formula: $\frac{d}{\mathrm{dx}} \sqrt{u} = \frac{1}{2 \sqrt{u}} \cdot \frac{d}{\mathrm{dx}} \left(u\right)$

$\frac{d}{\mathrm{dx}} \sqrt{x + 7} = \frac{d}{\mathrm{dx}} {\left(x + 7\right)}^{\frac{1}{2}} = \frac{1}{2} \cdot {\left(x + 7\right)}^{\frac{1}{2} - 1} \frac{d}{\mathrm{dx}} \left(x + 7\right)$
$= \frac{1}{2} \cdot {\left(x + 7\right)}^{- \frac{1}{2}} \cdot \left(1 + 0\right) = \frac{1}{2 \sqrt{x + 7}}$

God bless....I hope the explanation is useful