How do you find the first and second derivatives of #f(x)=(x-1)/(x+1)# using the quotient rule?
That is the first derivative. To find the second derivative, use the quotient rule on the first derivative.
Going back to finding the second derivative:
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To find the first and second derivatives of ( f(x) = \frac{x - 1}{x + 1} ) using the quotient rule:
First Derivative: [ f'(x) = \frac{(x + 1)(1) - (x - 1)(1)}{(x + 1)^2} ]
Second Derivative: [ f''(x) = \frac{(x + 1)(1) - (x - 1)(1)}{(x + 1)^2} - \frac{2(x - 1)((x + 1)(1) - (x - 1)(1))}{(x + 1)^3} ]
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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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