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

User Afinas EM
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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

User Tuvia Khusid
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