# How do you find the derivative of sqrt(2x+3)?

Jan 3, 2016

The derivative of this function is $\frac{1}{\sqrt{2 x + 3}}$.

#### Explanation:

Let $h \left(x\right) = \sqrt{2 x + 3}$. You see that that $h = f \circ g$ with $f \left(x\right) = \sqrt{x}$ and $g \left(x\right) = 2 x + 3$.

By the chain rule, $h ' \left(x\right) = g ' \left(x\right) \cdot \left(f ' \circ g\right) \left(x\right) = g ' \left(x\right) \cdot f ' \left(g \left(x\right)\right)$.

Here, $f ' \left(x\right) = \frac{1}{2 \sqrt{x}}$ and $g ' \left(x\right) = 2$.

So $h ' \left(x\right) = 2 \cdot \frac{1}{2 \sqrt{2 x + 3}} = \frac{1}{\sqrt{2 x + 3}}$