How do you find the derivative for #y= (2x) / (sqrt(x - 1))#?
You can use two approaches to differentiate this function.
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
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