# If #f(x)= 1/x # and #g(x) = 1/x #, how do you differentiate #f'(g(x)) # using the chain rule?

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To differentiate ( f'(g(x)) ) using the chain rule when ( f(x) = \frac{1}{x} ) and ( g(x) = \frac{1}{x} ), follow these steps:

- Find the derivative of ( f(x) ) with respect to its argument: ( f'(x) = -\frac{1}{x^2} ).
- Compute the derivative of ( g(x) ) with respect to ( x ): ( g'(x) = -\frac{1}{x^2} ).
- Substitute ( g(x) ) into ( f'(x) ): ( f'(g(x)) = -\frac{1}{(1/x)^2} = -\frac{1}{\frac{1}{x^2}} = -x^2 ).

Thus, the derivative of ( f'(g(x)) ) using the chain rule is ( -x^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.

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