Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^(4/5)
Derivative of x^2+5
Derivative of x^3-1/5*x^2+2*x-4
Derivative of |x-1|
Integral of d{x}:
(x^2+2)^2
Identical expressions
(x^ two + two)^ two
(x squared plus 2) squared
(x to the power of two plus two) to the power of two
(x2+2)2
x2+22
(x²+2)²
(x to the power of 2+2) to the power of 2
x^2+2^2
Similar expressions
(x^2-2)^2

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

Derivative of (x^2+2)^2

The solution

You have entered [src]

        2
/ 2    \ 
\x  + 2/

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

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

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

Transform

Detail solution

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

$2 x \left(2 x^{2} + 4\right)$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

Derivative of (x^2+2)^2