# Find the derivative of the function below by simplifying ? F(x) =( x - 7x √x) ÷ √x

Mar 24, 2017

$f ' \left(x\right) = \frac{1 - 14 \sqrt{x}}{2 \sqrt{x}}$

#### Explanation:

$f \left(x\right) = \frac{x - 7 x \sqrt{x}}{\sqrt{x}}$

Splitting up the fraction gives two distinct terms:

$\frac{x}{\sqrt{x}} = \frac{\sqrt{x} \sqrt{x}}{\sqrt{x}} = \sqrt{x}$

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

So:

$f \left(x\right) = \sqrt{x} - 7 x$

Which can be differentiated using the power rule:

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

$f ' \left(x\right) = \frac{1}{2} {x}^{- \frac{1}{2}} - 7 \left(1\right) {x}^{0}$

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

Finding a common denominator:

$f ' \left(x\right) = \frac{1 - 14 \sqrt{x}}{2 \sqrt{x}}$