How do you find the derivative of #1/(x^2) - 1/x#?

Answer 1

#-2/x^3+1/x^2#

This can be done with the quotient rule, but the easiest thing to do is to first rewrite:

#1/x^2-1/x = x^(-2)-x^(-1)#
#d/dx(1/x^2-1/x) = d/dx(x^(-2)-x^(-1)) = -2x^(-3) -(-1)x^(-2)# #=-2/x^3+1/x^2#
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Answer 2

To find the derivative of ( \frac{1}{x^2} - \frac{1}{x} ), you differentiate each term separately using the power rule and the rule for differentiating a constant multiple of a function. The derivative of ( \frac{1}{x^2} ) is ( -\frac{2}{x^3} ), and the derivative of ( \frac{1}{x} ) is ( -\frac{1}{x^2} ). Therefore, the derivative of the given expression is ( -\frac{2}{x^3} + \frac{1}{x^2} ).

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Answer from HIX Tutor

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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