# How do you differentiate # y= sqrt((3x)/(2x-3))# using the chain rule?

##### 1 Answer

The final answer, using the chain rule and the quotient rule is:

See below for the details.

#### Explanation:

I find this type of function much easier to handle without the radical sign, so I will rewrite it as

As usual with the chain rule, we begin with the "outermost" function (i.e., ask yourself, "If I wanted to find f(2), for example, what is the last function that I would do?). In this case, that is clearly the rational exponent (formerly the radical). Thus, I differentiate that first using the power rule, then handle the rational function using the quotient rule.

So: the answer becomes: