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1/2x^3-4x^2+6x-8
The derivative of the function/ 1/2x^3-4x^2+6x-8

Derivative of 1/2x^3-4x^2+6x-8

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 3                 
x       2          
-- - 4*x  + 6*x - 8
2
$$\frac{x^{3}}{2} - 4 x^{2} + 6 x - 8$$ 
  / 3                 \
d |x       2          |
--|-- - 4*x  + 6*x - 8|
dx\2                  /
$$\frac{d}{d x} \left(\frac{x^{3}}{2} - 4 x^{2} + 6 x - 8\right)$$
Transform
Detail solution

  1. Differentiate 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: goes to

      So, the result is:

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

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

        1. Apply the power rule: goes to

        So, the result is:

      So, the result is:

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

      1. Apply the power rule: goes to

      So, the result is:

    4. The derivative of the constant is zero.

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
             2
          3*x 
6 - 8*x + ----
           2
$$\frac{3 x^{2}}{2} - 8 x + 6$$
Simplify
The second derivative [src] 
-8 + 3*x
$$3 x - 8$$
Simplify
The third derivative [src] 
3
$$3$$
Simplify
3-th derivative [src] 
3
$$3$$
Simplify
The graph
Derivative of 1/2x^3-4x^2+6x-8
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