Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (x^2+1)^3
Derivative of (x^2-1)*(x^4+2)
Derivative of (x-1)/2
Derivative of sqrt(4-x^2)
Integral of d{x}:
(x^2+1)^3
Identical expressions
(x^ two + one)^ three
(x squared plus 1) cubed
(x to the power of two plus one) to the power of three
(x2+1)3
x2+13
(x²+1)³
(x to the power of 2+1) to the power of 3
x^2+1^3
Similar expressions
(x^2-1)^3

The derivative of the function/ (x^2+1)^3

Derivative of (x^2+1)^3

The solution

You have entered [src]

        3
/ 2    \ 
\x  + 1/

$$\left(x^{2} + 1\right)^{3}$$

(x^2 + 1)^3

Detail solution

Let $u = x^{2} + 1$ .
Apply the power rule: $u^{3}$ goes to $3 u^{2}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} + 1\right)$ :
1. Differentiate $x^{2} + 1$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $1$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$6 x \left(x^{2} + 1\right)^{2}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            2
    / 2    \ 
6*x*\x  + 1/

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

Simplify

The second derivative [src]

  /     2\ /       2\
6*\1 + x /*\1 + 5*x /

$$6 \left(x^{2} + 1\right) \left(5 x^{2} + 1\right)$$

Simplify

The third derivative [src]

     /       2\
24*x*\3 + 5*x /

$$24 x \left(5 x^{2} + 3\right)$$

Simplify

The graph

Derivative of (x^2+1)^3