How do you find the derivative of #y(x)= 6/(x-8)#?
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To find the derivative of ( y(x) = \frac{6}{x-8} ), you can use the quotient rule. The quotient rule 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} ]
In this case, ( u(x) = 6 ) and ( v(x) = x - 8 ). Taking the derivatives:
[ u'(x) = 0 ] (since 6 is a constant) [ v'(x) = 1 ] (the derivative of ( x - 8 ) is 1)
Now, applying the quotient rule:
[ \frac{d}{dx} \left( \frac{6}{x-8} \right) = \frac{(0)(x-8) - (6)(1)}{(x-8)^2} ]
[ = \frac{-6}{(x-8)^2} ]
So, the derivative of ( y(x) = \frac{6}{x-8} ) is ( y'(x) = \frac{-6}{(x-8)^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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