# How do you differentiate y = sqrt(x)(9 x - 8)?

Sep 8, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{27}{2} \sqrt{x} - \frac{8}{2 \sqrt{x}}$

#### Explanation:

Product rule states if $f \left(x\right) = g \left(x\right) h \left(x\right)$

then $\frac{\mathrm{df}}{\mathrm{dx}} = \frac{\mathrm{dg}}{\mathrm{dx}} \times h \left(x\right) + \frac{\mathrm{dh}}{\mathrm{dx}} \times g \left(x\right)$

Hence as $y = \sqrt{x} \left(9 x - 8\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 9 \times \sqrt{x} + \frac{1}{2 \sqrt{x}} \times \left(9 x - 8\right)$

= $9 \sqrt{x} + \frac{9 x}{2 \sqrt{x}} - \frac{8}{2 \sqrt{x}}$

= $9 \sqrt{x} + \frac{9}{2} \sqrt{x} - \frac{8}{2 \sqrt{x}}$

= $\frac{27}{2} \sqrt{x} - \frac{8}{2 \sqrt{x}}$