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(x^2+1)^3

Derivative of (x^2+1)^3

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
        3
/ 2    \ 
\x  + 1/ 
$$\left(x^{2} + 1\right)^{3}$$
(x^2 + 1)^3
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    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 of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
            2
    / 2    \ 
6*x*\x  + 1/ 
$$6 x \left(x^{2} + 1\right)^{2}$$
The second derivative [src]
  /     2\ /       2\
6*\1 + x /*\1 + 5*x /
$$6 \left(x^{2} + 1\right) \left(5 x^{2} + 1\right)$$
The third derivative [src]
     /       2\
24*x*\3 + 5*x /
$$24 x \left(5 x^{2} + 3\right)$$
The graph
Derivative of (x^2+1)^3