# How do you find the derivative of n(t) = 150 - 600/root3(16+3t^2)?

Jul 13, 2018

n'(t)=1200t/(root(3)(16+3t^2)^2

#### Explanation:

writing

$n \left(t\right) = 150 - 600 {\left(16 + 3 {t}^{2}\right)}^{- \frac{1}{3}}$
note that $\left(150\right) ' = 0$
and

$n ' \left(t\right) = - 600 \cdot \left(- \frac{1}{3}\right) {\left(16 + 3 {t}^{2}\right)}^{- \frac{2}{3}} 6 t$ simplifying we obtain

$n ' \left(t\right) = 1200 \frac{t}{\sqrt[3]{16 + 3 {t}^{2}}} ^ 2$