# What is the derivative of sqrt(7x)?

##### 2 Answers
Jan 16, 2016

$\frac{7}{2 \sqrt{7 x}}$

#### Explanation:

rewrite the function as: $\sqrt{7 x} = {\left(7 x\right)}^{\frac{1}{2}}$

applying the 'chain rule' : $\frac{1}{2} {\left(7 x\right)}^{- \frac{1}{2}} . \frac{d}{\mathrm{dx}} \left(7 x\right)$

= $\frac{1}{2} {\left(7 x\right)}^{- \frac{1}{2}} \left(7\right) = \frac{7}{2 \sqrt{7 x}}$

Jan 16, 2016

$\frac{\sqrt{7}}{2 \sqrt{x}}$, or, if you disapprove of radicals in the denominator, it is $\frac{\sqrt{7 x}}{2 x}$

#### Explanation:

$\sqrt{7 x} = \sqrt{7} \sqrt{x}$ and $\frac{d}{\mathrm{dx}} \left(\sqrt{x}\right) = \frac{1}{2 \sqrt{x}}$.

Therefore,

$\frac{d}{\mathrm{dx}} \left(\sqrt{7 x}\right) = \sqrt{7} \frac{d}{\mathrm{dx}} \left(\sqrt{x}\right) = \sqrt{7} \left(\frac{1}{2 \sqrt{x}}\right) = \frac{\sqrt{7}}{2 \sqrt{x}}$.

Eliminate the square root from the denominator if necessary.