How do you find the derivative of (x-1)/(x+1)?

1 Answer
Feb 25, 2016

2/(x+1)^2

Explanation:

Use the quotient rule, which states that

d/dx(f(x)/g(x))=(g(x)f'(x)-f(x)g'(x))/g(x)^2

Here, we see that

f(x)=x-1
g(x)=x+1

So both their derivatives equal

f'(x)=1
g'(x)=1

Thus, using the first equation,

d/dx((x-1)/(x+1))=((x+1)(1)-(x-1)(1))/(x+1)^2

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