# How do you find the slope of a tangent line to the graph of the function #y=e^- x/(x+1)#, at x=1?

Applying the quotient rule

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To find the slope of a tangent line to the graph of a function at a specific point, you can use the derivative of the function.

To find the derivative of the function y=e^(-x)/(x+1), you can use the quotient rule.

The derivative of y with respect to x is given by:

dy/dx = [(x+1)(-e^(-x)) - e^(-x)(1)] / (x+1)^2

To find the slope of the tangent line at x=1, substitute x=1 into the derivative:

dy/dx = [(1+1)(-e^(-1)) - e^(-1)(1)] / (1+1)^2

Simplifying this expression will give you the slope of the tangent line at x=1.

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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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