How do you differentiate y = 2 / [3sqrt(x^2 - 5x)] ?

Jan 30, 2016

$\frac{4 x - 10}{3 \sqrt{{\left({x}^{2} - 5 x\right)}^{3}}}$

Explanation:

Here,
$y = \frac{2}{3 \sqrt{{x}^{2} - 5 x}}$

so,
$\frac{\mathrm{dy}}{\mathrm{dx}}$

$= \frac{d}{\mathrm{dx}} \left(\frac{2}{3 \sqrt{{x}^{2} - 5 x}}\right)$

$= \frac{2}{3} \frac{d}{\mathrm{dx}} \left(\frac{1}{\sqrt{{x}^{2} - 5 x}}\right)$

$= \frac{2}{3} \cdot \frac{1}{{\left({x}^{2} - 5 x\right)}^{\frac{3}{2}}} \frac{d}{\mathrm{dx}} \left({x}^{2} - 5 x\right)$

$= \frac{2}{3} \cdot \frac{1}{{\left({x}^{2} - 5 x\right)}^{\frac{3}{2}}} \left(2 x - 5\right)$

$= \frac{4 x - 10}{3 \sqrt{{\left({x}^{2} - 5 x\right)}^{3}}}$