Mister Exam

Other calculators

Derivative of 4*x^3-16*x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3       
4*x  - 16*x
4x316x4 x^{3} - 16 x
4*x^3 - 16*x
Detail solution
  1. Differentiate 4x316x4 x^{3} - 16 x term by term:

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: x3x^{3} goes to 3x23 x^{2}

      So, the result is: 12x212 x^{2}

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: xx goes to 11

      So, the result is: 16-16

    The result is: 12x21612 x^{2} - 16


The answer is:

12x21612 x^{2} - 16

The graph
02468-8-6-4-2-1010-1000010000
The first derivative [src]
          2
-16 + 12*x 
12x21612 x^{2} - 16
The second derivative [src]
24*x
24x24 x
The third derivative [src]
24
2424