How do you find the derivative of #(x-1)/(x+1)#?
Use the quotient rule, which states that
Here, we see that
So both their derivatives equal
Thus, using the first equation,
By signing up, you agree to our Terms of Service and Privacy Policy
To find the derivative of (\frac{x-1}{x+1}), you can use the quotient rule. The quotient rule states that if you have a function (u(x)) divided by another function (v(x)), the derivative is given by the formula:
[ \left( \frac{u}{v} \right)' = \frac{u'v - uv'}{v^2} ]
Where (u') represents the derivative of (u) with respect to (x) and (v') represents the derivative of (v) with respect to (x).
Applying this rule to (\frac{x-1}{x+1}), we have:
[ u(x) = x - 1 ] [ v(x) = x + 1 ]
Taking the derivatives:
[ u'(x) = 1 ] [ v'(x) = 1 ]
Now plug these into the quotient rule formula:
[ \frac{(x-1)(1) - (x+1)(1)}{(x+1)^2} ]
Simplify the numerator:
[ (x-1) - (x+1) = x - 1 - x - 1 = -2 ]
So the derivative of (\frac{x-1}{x+1}) is:
[ \frac{-2}{(x+1)^2} ]
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7