# How do you differentiate #f(x)= (x-1)/(x+1)^3# using the quotient rule?

You've got to use both the quotient rule and the chain rule together, giving you

Now with the knowledge of the derivatives of u and v, you can differentiate the function using the quotient rule by substituting in the v and u values:

After simplifying, this gives:

Which is your final answer.

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To differentiate ( f(x) = \frac{{x - 1}}{{(x + 1)^3}} ) using the quotient rule, follow these steps:

- Identify ( u(x) ) as the numerator and ( v(x) ) as the denominator.
- Apply the quotient rule: ( f'(x) = \frac{{u'(x)v(x) - u(x)v'(x)}}{{[v(x)]^2}} ).
- Find ( u'(x) ) and ( v'(x) ).
- Substitute the values into the quotient rule formula.
- Simplify the expression.

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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.

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