# How do you find the derivative of #f(x)=x^3 - 5x^2 - 4x + 20#?

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To find the derivative of ( f(x) = x^3 - 5x^2 - 4x + 20 ), you differentiate each term separately using the power rule for derivatives:

- For ( x^3 ), the derivative is ( 3x^{3-1} = 3x^2 ).
- For ( -5x^2 ), the derivative is ( -5(2)x^{2-1} = -10x ).
- For ( -4x ), the derivative is ( -4(1)x^{1-1} = -4 ).
- The derivative of a constant (like ( 20 )) is ( 0 ).

Putting these together, the derivative of ( f(x) ) is:

[ f'(x) = 3x^2 - 10x - 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.

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