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y=(x^2+3x)(x-1)

Derivative of y=(x^2+3x)(x-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
/ 2      \        
\x  + 3*x/*(x - 1)
$$\left(x - 1\right) \left(x^{2} + 3 x\right)$$
(x^2 + 3*x)*(x - 1)
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      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:

      The result is:

    ; 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:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 2                          
x  + 3*x + (3 + 2*x)*(x - 1)
$$x^{2} + 3 x + \left(x - 1\right) \left(2 x + 3\right)$$
The second derivative [src]
2*(2 + 3*x)
$$2 \left(3 x + 2\right)$$
The third derivative [src]
6
$$6$$
The graph
Derivative of y=(x^2+3x)(x-1)