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

The quotient rule states that for

Derivating it following the quotient rule, then:

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

- Identify ( u = 1 + 2x ) and ( v = -x^2 + 1 ).
- Apply the quotient rule formula: ( f'(x) = \frac{v(u') - u(v')}{v^2} ).
- Calculate ( u' ) and ( v' ).
- Substitute the values into the quotient rule formula and simplify to get the derivative ( f'(x) ).

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

- 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 these values into the quotient rule formula.
- Simplify the expression to get the derivative.

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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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