Question

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

Answer 1

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

Explanation:

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`

Answer 2

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

Explanation:

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

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

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

Answer 3

`3x^2-6x`

Explanation:

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!