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x^3/6-0.5x^2-3x+2
The derivative of the function/ x^3/6-0.5x^2-3x+2

You entered:

x^3/6-0.5x^2-3x+2

What you mean?

x^3/6 - x^2/2 - 3*x + 2
 
sqrt(x) - x^2/2 - 3*x + 2
 
sqrt(x) - x^2/2 - 3*x + 2

Derivative of x^3/6-0.5x^2-3x+2

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

The graph:

from to

Piecewise:

The solution

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

    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    
     x     
-3 + -- - x
     2
$$\frac{x^{2}}{2} - x - 3$$
Simplify
The second derivative [src] 
-1 + x
$$x - 1$$
Simplify
The third derivative [src] 
1
$$1$$
Simplify
The graph
Derivative of x^3/6-0.5x^2-3x+2
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