How do you find the derivative of #f(x)=1/(x+2)#?
Applying power rule,
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To find the derivative of ( f(x) = \frac{1}{x+2} ), use the quotient rule, which states that for functions ( u(x) ) and ( v(x) ), the derivative of ( \frac{u(x)}{v(x)} ) is given by:
[ \frac{d}{dx}\left(\frac{u(x)}{v(x)}\right) = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2} ]
Applying this rule to ( f(x) = \frac{1}{x+2} ), where ( u(x) = 1 ) and ( v(x) = x + 2 ), we have:
[ u'(x) = 0 ] [ v'(x) = 1 ]
Substituting into the quotient rule formula:
[ \frac{d}{dx}\left(\frac{1}{x+2}\right) = \frac{0(x+2) - 1(1)}{(x+2)^2} ] [ = \frac{-1}{(x+2)^2} ]
So, the derivative of ( f(x) = \frac{1}{x+2} ) is ( -\frac{1}{(x+2)^2} ).
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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.
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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