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

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

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

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The solution

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

  1. Differentiate term by term:

    1. The derivative of the constant is zero.

    2. 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:

    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 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:

    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 
-1 + x - ----
          2
$$- \frac{3 x^{2}}{2} + x - 1$$
Simplify
The second derivative [src] 
1 - 3*x
$$1 - 3 x$$
Simplify
The third derivative [src] 
-3
$$-3$$
Simplify
The graph
Derivative of 6-x+1/2x^2-1/2x^3
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