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What is the derivative of #f(x) = x^3 - 3x^2 - 1#?

Answer 1

Paisley Johnson

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

We need the sum rule #(u+v+w)'=u'+v'+w'# and that

#(x^n)'=nx^(n-1)#

so we get

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

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Answer 2

Christopher Agresta

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

#"differentiate each term using the "color(blue)"power rule"#

#•color(white)(x)d/dx(ax^n)=nax^(n-1)#

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

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Answer 3

Aurora Alvarado

#3x^2-6x#

The derivative of a sum/difference is the same as the sum/difference of the derivatives, so we can take the derivative of all of these terms.

We can use the Power Rule- here, the exponent is brought out front, and the power is decremented by #1#. We get

#3x^2-6x#

Recall that the derivative of a constant is zero.

Hope this helps!

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Answer 4

Emily Ammerman

The derivative of ( f(x) = x^3 - 3x^2 - 1 ) is ( f'(x) = 3x^2 - 6x ).

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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.