If #f(x)= 1/x # and #g(x) = 1/x #, what is #f'(g(x)) #?
I'll assume no error in the statement of the question.
Therefore,
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To find ( f'(g(x)) ), we need to find the derivative of ( f ) with respect to ( g(x) ) and then multiply it by the derivative of ( g(x) ) with respect to ( x ).
Given ( f(x) = \frac{1}{x} ) and ( g(x) = \frac{1}{x} ), the derivative of ( f(x) ) with respect to ( x ) is ( f'(x) = -\frac{1}{x^2} ).
Now, since ( g(x) = \frac{1}{x} ), the derivative of ( g(x) ) with respect to ( x ) is ( g'(x) = -\frac{1}{x^2} ).
So, ( f'(g(x)) = f'(x) \cdot g'(x) = (-\frac{1}{x^2}) \cdot (-\frac{1}{x^2}) = \frac{1}{x^4} ).
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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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