# How to find instantaneous rate of change for #y(x)=1/(x+2)# at x=2?

At x = 2, y(x)'s instantaneous rate of change is y'(2).

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To find the instantaneous rate of change for ( y(x) = \frac{1}{x+2} ) at ( x = 2 ), we can use the concept of the derivative.

The derivative of a function represents the rate at which the function is changing at any given point.

To find the derivative of ( y(x) ), we'll use the power rule for differentiation:

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

Now, we can evaluate the derivative at ( x = 2 ) to find the instantaneous rate of change:

[ y'(x) = -\frac{1}{{(2+2)}^2} = -\frac{1}{16} ]

So, the instantaneous rate of change for ( y(x) = \frac{1}{x+2} ) at ( x = 2 ) is ( -\frac{1}{16} ).

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