# How do you find the derivative of root3((6x+7))?

First, recognize that you are looking at the cube root of $\left(6 x + 7\right)$, which can be rewritten as ${\left(6 x + 7\right)}^{\frac{1}{3}}$. Then you will need to use the chain rule to take the derivative.
To do this, you would first bring down the power of $\frac{1}{3}$ and reduce the power by one. This results in $\frac{1}{3} {\left(6 x + 7\right)}^{- \frac{2}{3}}$. Then, multiply this by the derivative of the term inside the parentheses, which is just 6 (the derivative of a constant is zero).
Your final simplified answer is $2 {\left(6 x + 7\right)}^{- \frac{2}{3}}$.