# How do you differentiate #f(x)=x/(x-1)^2+x^2-4/(1-1x)# using the sum rule?

By signing up, you agree to our Terms of Service and Privacy Policy

To differentiate ( f(x) = \frac{x}{(x - 1)^2} + \frac{x^2 - 4}{1 - x} ) using the sum rule:

- Differentiate each term separately.
- Apply the sum rule to combine the derivatives.

Given ( f(x) = \frac{x}{(x - 1)^2} + \frac{x^2 - 4}{1 - x} ), let's differentiate each term:

For the first term, ( \frac{x}{(x - 1)^2} ):

- Apply the quotient rule.
- ( u = x ) and ( v = (x - 1)^2 ).
- Differentiate ( u ) and ( v ) separately.

[ \frac{d}{dx} \left( \frac{x}{(x - 1)^2} \right) = \frac{u'v - uv'}{v^2} ]

For the second term, ( \frac{x^2 - 4}{1 - x} ):

- Apply the quotient rule.
- ( u = x^2 - 4 ) and ( v = 1 - x ).
- Differentiate ( u ) and ( v ) separately.

[ \frac{d}{dx} \left( \frac{x^2 - 4}{1 - x} \right) = \frac{u'v - uv'}{v^2} ]

Once you have the derivatives of each term, apply the sum rule:

[ f'(x) = \frac{d}{dx} \left( \frac{x}{(x - 1)^2} \right) + \frac{d}{dx} \left( \frac{x^2 - 4}{1 - x} \right) ]

Finally, simplify the resulting expression to obtain ( f'(x) ).

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.

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