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Derivative of:
Derivative of e^-1
Derivative of 2*x^5
Derivative of f(x)=1
Derivative of (x+8)^2
Integral of d{x}:
(x^2+1)^4
Identical expressions
(x^ two + one)^ four
(x squared plus 1) to the power of 4
(x to the power of two plus one) to the power of four
(x2+1)4
x2+14
(x²+1)⁴
(x to the power of 2+1) to the power of 4
x^2+1^4
Similar expressions
(x^2-1)^4

The derivative of the function/ (x^2+1)^4

Derivative of (x^2+1)^4

The solution

You have entered [src]

        4
/ 2    \ 
\x  + 1/

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

  /        4\
d |/ 2    \ |
--\\x  + 1/ /
dx

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

Transform

Detail solution

Let $u = x^{2} + 1$ .
Apply the power rule: $u^{4}$ goes to $4 u^{3}$
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:

$8 x \left(x^{2} + 1\right)^{3}$
Now simplify:

$8 x \left(x^{2} + 1\right)^{3}$

The answer is:

$8 x \left(x^{2} + 1\right)^{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$8 x \left(x^{2} + 1\right)^{3}$$

Simplify

The second derivative [src]

          2           
  /     2\  /       2\
8*\1 + x / *\1 + 7*x /

$$8 \left(x^{2} + 1\right)^{2} \cdot \left(7 x^{2} + 1\right)$$

Simplify

The third derivative [src]

     /     2\ /       2\
48*x*\1 + x /*\3 + 7*x /

$$48 x \left(x^{2} + 1\right) \left(7 x^{2} + 3\right)$$

Simplify

The graph

Derivative of (x^2+1)^4