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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.

1 Answers 1

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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.

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    How does (1-x)^4 = (x-1)^4? The rest is making sense, though that part is kinda puzzling. – 2017-01-19
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    $(1-x)^4=1^4(1-x)^4=(-1)^4(1-x)^4=(x-1)^4.$ :) – 2017-01-19
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    Oh, right! Silly thinking on my part – 2017-01-19