# How do you find the derivative of y=3/4(x^(2)-1)^(2/3)?

Feb 27, 2016

$f ' \left(x\right) = \frac{x}{\sqrt[3]{{x}^{2} - 1}}$

#### Explanation:

$f \left(x\right) = \frac{3}{4} {\left({x}^{2} - 1\right)}^{\frac{2}{3}}$

Derivative:
$f ' \left(x\right) = \frac{3}{4} \cdot \frac{2}{3} \cdot {\left({x}^{2} - 1\right)}^{- \frac{1}{3}} \cdot 2 x$

$\textcolor{b l u e}{f ' \left(x\right) = \frac{x}{\sqrt[3]{{x}^{2} - 1}}}$

Steps:

$1 \text{ }$ $\frac{3}{4}$ is a constant so we can bring that out.

$2 \text{ }$ Using Power Rule, we can get $\frac{2}{3} {\left({x}^{2} - 1\right)}^{- \frac{1}{3}}$. However, since $\left({x}^{2} - 1\right)$ isn't $x$, we have to use Chain Rule.

$3 \text{ }$ We get the derivative of $\left({x}^{2} - 1\right)$ which is $2 x$ and multiply it.

Sorry, I'm not very good at explaining this. Just let me know if you have questions.