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

Answer 1

Samantha Adkison

#f'(x)=3x^2-1#

#f'(x)=3x^2-1#-> Use Power Rule; If #y=x^n# then #y'=nx^(n-1)#

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Answer 2

Charles Anctil

To find the derivative of ( f(x) = x^3 - x ), apply the power rule for differentiation. The power rule states that if ( f(x) = x^n ), then ( f'(x) = nx^{n-1} ). Using this rule, the derivative of ( x^3 ) is ( 3x^2 ), and the derivative of ( -x ) is ( -1 ). So, the derivative of ( f(x) = x^3 - x ) is ( f'(x) = 3x^2 - 1 ).

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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.