Mister Exam

Derivative of y=(x²+1)³

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

You have entered [src]
        3
/ 2    \ 
\x  + 1/ 
(x2+1)3\left(x^{2} + 1\right)^{3}
(x^2 + 1)^3
Detail solution
  1. Let u=x2+1u = x^{2} + 1.

  2. Apply the power rule: u3u^{3} goes to 3u23 u^{2}

  3. Then, apply the chain rule. Multiply by ddx(x2+1)\frac{d}{d x} \left(x^{2} + 1\right):

    1. Differentiate x2+1x^{2} + 1 term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      2. The derivative of the constant 11 is zero.

      The result is: 2x2 x

    The result of the chain rule is:

    6x(x2+1)26 x \left(x^{2} + 1\right)^{2}

  4. Now simplify:

    6x(x2+1)26 x \left(x^{2} + 1\right)^{2}


The answer is:

6x(x2+1)26 x \left(x^{2} + 1\right)^{2}

The graph
02468-8-6-4-2-1010-20000002000000
The first derivative [src]
            2
    / 2    \ 
6*x*\x  + 1/ 
6x(x2+1)26 x \left(x^{2} + 1\right)^{2}
The second derivative [src]
  /     2\ /       2\
6*\1 + x /*\1 + 5*x /
6(x2+1)(5x2+1)6 \left(x^{2} + 1\right) \left(5 x^{2} + 1\right)
The third derivative [src]
     /       2\
24*x*\3 + 5*x /
24x(5x2+3)24 x \left(5 x^{2} + 3\right)
The graph
Derivative of y=(x²+1)³