Find $\frac{dy}{dx}$, given y=fraction

Question

Using the Chain Rule, given $y=f(x)=\frac{(x+1)^5}{(1-x)^4}$

Find $\frac{dy}{dx}$.

I've never encountered a problem like this before, any tips on how to start solving would be greatly appreciated.

Answer 1

First of all, $(1-x)^4=(x-1)^4$ so $f(x)=\frac{(x+1)^5}{(x-1)^4}.$

Then, just use quotient rule, noting that by the chain rule we can treat the x+1s without adding anything onto them as the derivative of x+1 or x-1 is 1.

So, $f'(x)=\frac{(x-1)^45(x+1)^4-(x+1)^54(x-1)^3}{(x-1)^8}$ which can be simplified easy to get an answer.