# How do you differentiate f(x)=1/(x^7-2) using the quotient rule?

Nov 21, 2015

${y}^{'} = \frac{7 {x}^{6}}{{x}^{7} - 2} ^ 2$

#### Explanation:

While you can use the quotient rule, it's much more expedient to use the chain rule or log derivating, in my opinion, bypassing the need of remembering the formula. Nonetheless, the formula for the quotient formula goes as follows:

For

$y = \frac{u}{v}$ and $v \ne 0$

${y}^{'} = \frac{{u}^{'} v - {v}^{'} u}{v} ^ 2$

So we have

${y}^{'} = \frac{0 \cdot \left({x}^{7} - 2\right) - \left(7 {x}^{6}\right) \cdot 1}{{x}^{7} - 2} ^ 2 = \frac{7 {x}^{6}}{{x}^{7} - 2} ^ 2$