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Derivative of:
Derivative of e^(5*x)
Derivative of x/5
Derivative of (x^2+1)^2
Derivative of sin(1/x)
Integral of d{x}:
(x^2+1)^2
Identical expressions
(x^ two + one)^ two
(x squared plus 1) squared
(x to the power of two plus one) to the power of two
(x2+1)2
x2+12
(x²+1)²
(x to the power of 2+1) to the power of 2
x^2+1^2
Similar expressions
(x^2-1)^2

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

Derivative of (x^2+1)^2

The solution

You have entered [src]

        2
/ 2    \ 
\x  + 1/

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

(x^2 + 1)^2

Detail solution

Let $u = x^{2} + 1$ .
Apply the power rule: $u^{2}$ goes to $2 u$
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:

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

$4 x \left(x^{2} + 1\right)$

The answer is:

$4 x \left(x^{2} + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    / 2    \
4*x*\x  + 1/

$$4 x \left(x^{2} + 1\right)$$

Simplify

The second derivative [src]

  /       2\
4*\1 + 3*x /

$$4 \left(3 x^{2} + 1\right)$$

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

Derivative of (x^2+1)^2