# How do you find the derivative for #y= (2x) / (sqrt(x - 1))#?

##### 1 Answer

You can use two approaches to differentiate this function.

#### Explanation:

A very important thing to notice about this function is that you can write both as a *quotient* of two other functions, let's say *product* of two functions,

This means that you can approach it in two different ways, either by using the product rule or by using the quotient rule.

The chain rule will be needed in both cases, though.

To keep the answer from becoming too long, I will only show you one of the two approaches.

So, your function can be written as

The quotient rule allows you to differentiate this function by using

This means that you have

You can calculate

This will get you

Your target derivative will now be

You can simplify this by using fractional exponents

The starting point for the product rule approach would have been