# What is the derivative of (x + 1)/y?

##### 1 Answer
Aug 15, 2015

$\frac{d}{\mathrm{dx}} \left(\frac{x + 1}{y}\right) = \frac{y - \left(x + 1\right) \frac{\mathrm{dy}}{\mathrm{dx}}}{y} ^ 2$

#### Explanation:

Use the quotient rule and the chain rule. (all implicit differentiation uses the chain rule.)

$\frac{d}{\mathrm{dx}} \left(\frac{x + 1}{y}\right) = \frac{\left(1\right) y - \left(x + 1\right) \frac{\mathrm{dy}}{\mathrm{dx}}}{y} ^ 2$

There's not much more we can do without the rest of the equation relating $x$ and $y$.

We could rewrite a bit, to get:

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

or

$= \frac{1}{y} - \frac{x + 1}{y} ^ 2 \frac{\mathrm{dy}}{\mathrm{dx}}$