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Identical expressions
((x+ two /x- one))^ two
((x plus 2 divide by x minus 1)) squared
((x plus two divide by x minus one)) to the power of two
((x+2/x-1))2
x+2/x-12
((x+2/x-1))²
((x+2/x-1)) to the power of 2
x+2/x-1^2
((x+2 divide by x-1))^2
Similar expressions
((x+2/x+1))^2
((x-2/x-1))^2

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

Derivative of ((x+2/x-1))^2

The solution

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           2
/    2    \ 
|x + - - 1| 
\    x    /

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

(x + 2/x - 1)^2

Detail solution

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

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

$2 x - 2 + \frac{4}{x^{2}} - \frac{8}{x^{3}}$

The answer is:

$2 x - 2 + \frac{4}{x^{2}} - \frac{8}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

   /                  2\
   |         -1 + x + -|
   |    2             x|
24*|1 - -- - ----------|
   |     2       x     |
   \    x              /
------------------------
            3           
           x

$$\frac{24 \left(1 - \frac{x - 1 + \frac{2}{x}}{x} - \frac{2}{x^{2}}\right)}{x^{3}}$$

Simplify

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Derivative of ((x+2/x-1))^2

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The solution