# How do you differentiate #f(x)=x/(x+3)^2# using the quotient rule?

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To differentiate ( f(x) = \frac{x}{(x+3)^2} ) using the quotient rule:

- Identify the numerator and the denominator: ( u(x) = x ) and ( v(x) = (x+3)^2 ).
- Apply the quotient rule formula: ( f'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2} ).
- Find the derivatives of the numerator and the denominator: ( u'(x) = 1 ) and ( v'(x) = 2(x+3) ).
- Substitute these values into the quotient rule formula: ( f'(x) = \frac{(1)(x+3)^2 - (x)(2(x+3))}{(x+3)^4} ).
- Simplify the expression: ( f'(x) = \frac{(x+3)^2 - 2x(x+3)}{(x+3)^4} ).
- Expand and simplify further if necessary.

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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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