Question

F(X) = x^3 - 13x - 12

Answer 1

The derivative of the given expression,
`F(x) = x^3\ -\ 13x - 12`, is
`3x^(2)\ -\ 13`

How to obtain the derivative of
`F(x) = x^3\ -\ 13x - 12`?

To obtain the derivative of the expression given, we shall differential each term in the expression. This is shown below:

• Expression from the question:
  `F(x) = x^3\ -\ 13x - 12`
• Derivative of expression =?

We know that if
`y = ax^n`, then the derivative of y is written as:

`(dy)/(dx) = n\cdot ax^(n-1)`

We shall apply the above logic to obtain the derivative of
`F(x) = x^3\ -\ 13x - 12`. Details below:

`f(x) = x^3\ -\ 13x\ -\ 12\\\\f^(')(x) = 3\cdot x^(3-1)\ -\ 13\cdot x^(1-1)\ -\ 0\\\\f^(')(x) = 3x^(2)\ -\ 13x^(0)\\\\Recall:\\\\A^0 = 1\\\\Thus,\ we\ have:\\\\f^(')(x) = 3x^(2)\ -\ 13\\\\`

From the above, the derivative of
`F(x) = x^3\ -\ 13x - 12`, is
`3x^(2)\ -\ 13`

Complete question:

Find the derivative, given that F(x) = x^3 - 13x – 12