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Derivative of:
Derivative of 1/x^6
Derivative of x+lnx
Derivative of x^2-4*x+3
Derivative of -(x^2+324)/x
Integral of d{x}:
(1+x^2)^2
Limit of the function:
(1+x^2)^2
Identical expressions
(one +x^ two)^ two
(1 plus x squared ) squared
(one plus x to the power of two) to the power of two
(1+x2)2
1+x22
(1+x²)²
(1+x to the power of 2) to the power of 2
1+x^2^2
Similar expressions
(1-x^2)^2

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

Derivative of (1+x^2)^2

The solution

You have entered [src]

        2
/     2\ 
\1 + x /

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

(1 + x^2)^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. The derivative of the constant $1$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  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*\1 + x /

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

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 (1+x^2)^2