# What is the derivative of (5x+6)^(1/2)?

##### 2 Answers
Jun 10, 2018

${f}^{'} \left(x\right) = \frac{5}{2 \sqrt{5 x + 6}}$

#### Explanation:

$f \left(x\right) = {\left(5 x + 6\right)}^{\frac{1}{2}}$

${f}^{'} \left(x\right) = \frac{1}{2} {\left(5 x + 6\right)}^{\frac{1}{2} - 1} \cdot 5$ or

${f}^{'} \left(x\right) = \frac{1}{2} {\left(5 x + 6\right)}^{- \frac{1}{2}} \cdot 5$ or

${f}^{'} \left(x\right) = \frac{5}{2 \sqrt{5 x + 6}}$ [Ans]

Jun 10, 2018

$\frac{5}{2 {\left(5 x + 6\right)}^{\frac{1}{2}}}$

#### Explanation:

$\text{differentiate using the "color(blue)"chain rule}$

$\text{given "y=f(g(x))" then}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = f ' \left(g \left(x\right)\right) \times g ' \left(x\right) \leftarrow \textcolor{b l u e}{\text{chain rule}}$

$\frac{d}{\mathrm{dx}} \left({\left(5 x + 6\right)}^{\frac{1}{2}}\right)$

$= \frac{1}{2} {\left(5 x + 6\right)}^{- \frac{1}{2}} \times \frac{d}{\mathrm{dx}} \left(5 x + 6\right)$

$= \frac{5}{2 {\left(5 x + 6\right)}^{\frac{1}{2}}}$