How do you find the derivative of (x-1)/(x+1)?
1 Answer
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
color(white)(XXXX.lXX)=2/(x+1)^2