# How do you find the derivative of the function: #f(x) = x^3 - 3x^2 - 1#?

This function involves the most commonly used rule for taking derivatives: the Power Rule. It states that whenever you have a power for a variable, that is automatically considered a product of the variable with the power being subtracted by one. Here is a general form:

Solving for the equation gives you the same answer (though a long work process). The Power Rule and other rules for derivatives give you the shortcuts to solve for even the most complicated problems in using the Limit Definition.

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To find the derivative of the function f(x) = x^3 - 3x^2 - 1, you can use the power rule for differentiation. The power rule states that if you have a term of the form ax^n, the derivative is n * ax^(n-1). Applying this rule to each term of the function, the derivative of f(x) with respect to x is:

f'(x) = 3x^2 - 6x

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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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