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x(x^3+4x^2-1)

Derivative of x(x^3+4x^2-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  / 3      2    \
x*\x  + 4*x  - 1/
$$x \left(x^{3} + 4 x^{2} - 1\right)$$
d /  / 3      2    \\
--\x*\x  + 4*x  - 1//
dx                   
$$\frac{d}{d x} x \left(x^{3} + 4 x^{2} - 1\right)$$
Detail solution
  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 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 the constant is zero.

      The result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
      3      2     /   2      \
-1 + x  + 4*x  + x*\3*x  + 8*x/
$$x^{3} + 4 x^{2} + x \left(3 x^{2} + 8 x\right) - 1$$
The second derivative [src]
2*x*(12 + 6*x)
$$2 x \left(6 x + 12\right)$$
The third derivative [src]
6*(4 + 4*x)
$$6 \cdot \left(4 x + 4\right)$$
The graph
Derivative of x(x^3+4x^2-1)