Find the derivative of [(2+x)/(x-3)]^(2/5)

Question

I tried the power of a function rule, quotient rule, the chain rule but keep getting stuck.

Answer 1

Yes, you have to use the chain rule here.

Step one:

Take [(2+x)/(x-3)] as y.
d(y^2/5)/dx = (2/5)y^(-3/5), as per the exponent rule for differentiation.

Next, apply the quotient rule on [(2+x)/(x-3)] to get its derivative.

Multiply the answer obtained in both steps for the final answer.

Answer 2

I got (2/5)[(2+x/x-3)^(-3/5)] (-5/(x-3)^2)

Now I am having troubles simplifying it.