Mister Exam

Derivative of (x³-2)(x²+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/
$$\left(x^{2} + 1\right) \left(x^{3} - 2\right)$$
(x^3 - 2)*(x^2 + 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 the constant is zero.

      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]
    / 3    \      2 / 2    \
2*x*\x  - 2/ + 3*x *\x  + 1/
$$3 x^{2} \left(x^{2} + 1\right) + 2 x \left(x^{3} - 2\right)$$
The second derivative [src]
  /        3       /     2\\
2*\-2 + 7*x  + 3*x*\1 + x //
$$2 \left(7 x^{3} + 3 x \left(x^{2} + 1\right) - 2\right)$$
The third derivative [src]
  /        2\
6*\1 + 10*x /
$$6 \left(10 x^{2} + 1\right)$$