Mister Exam

Other calculators


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

Derivative of y=x^3(2x^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 *\2*x  - 1/
$$x^{3} \cdot \left(2 x^{2} - 1\right)$$
d / 3 /   2    \\
--\x *\2*x  - 1//
dx               
$$\frac{d}{d x} x^{3} \cdot \left(2 x^{2} - 1\right)$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Differentiate term by term:

      1. 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 the constant is zero.

      The result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   4      2 /   2    \
4*x  + 3*x *\2*x  - 1/
$$4 x^{4} + 3 x^{2} \cdot \left(2 x^{2} - 1\right)$$
The second derivative [src]
    /         2\
2*x*\-3 + 20*x /
$$2 x \left(20 x^{2} - 3\right)$$
The third derivative [src]
  /         2\
6*\-1 + 20*x /
$$6 \cdot \left(20 x^{2} - 1\right)$$
The graph
Derivative of y=x^3(2x^2-1)