# What is the first derivative of the curve described by y = 1/2root(3)(x) + 8/x + 1?

Nov 21, 2016

First of all, we can rewrite the curve as

$y = \frac{1}{2} {x}^{\frac{1}{3}} + 8 {x}^{- 1} + 1$

Differentiate using the power rule, $\left({x}^{n}\right) ' = n {x}^{n - 1}$.

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{3} \left(\frac{1}{2}\right) {x}^{- \frac{2}{3}} + \left(- 1\right) 8 {x}^{- 2} + 0$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{6 {x}^{\frac{2}{3}}} - \frac{8}{x} ^ 2$

Hopefully this helps!