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(1/9)*x^3*(x+4)
The derivative of the function/ (1/9)*x^3*(x+4)

Derivative of (1/9)*x^3*(x+4)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 3        
x *(x + 4)
----------
    9
$$\frac{x^{3} \left(x + 4\right)}{9}$$ 
  / 3        \
d |x *(x + 4)|
--|----------|
dx\    9     /
$$\frac{d}{d x} \frac{x^{3} \left(x + 4\right)}{9}$$
Transform
Detail solution

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

    1. Apply the product rule:

      ; to find :

      1. Apply the power rule: goes to

      ; to find :

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of the constant is zero.

        The result is:

      The result is:

    So, the result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 3    2        
x    x *(x + 4)
-- + ----------
9        3
$$\frac{x^{3}}{9} + \frac{x^{2} \left(x + 4\right)}{3}$$
Simplify
The second derivative [src] 
2*x*(4 + 2*x)
-------------
      3
$$\frac{2 x \left(2 x + 4\right)}{3}$$
Simplify
The third derivative [src] 
8*(1 + x)
---------
    3
$$\frac{8 \left(x + 1\right)}{3}$$
Simplify
The graph
Derivative of (1/9)*x^3*(x+4)
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