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Derivative of:
Derivative of x+3
Derivative of sqrt(x^2+1)
Derivative of 1/sin(x)
Derivative of x^x^2
Identical expressions
y=x- two sqrt(x-2)
y equally x minus 2 square root of (x minus 2)
y equally x minus two square root of (x minus 2)
y=x-2√(x-2)
y=x-2sqrtx-2
Similar expressions
y=x-2sqrt(x+2)
y=x+2sqrt(x-2)

The derivative of the function/ y=x-2sqrt(x-2)

Derivative of y=x-2sqrt(x-2)

The solution

You have entered [src]

        _______
x - 2*\/ x - 2

$$x - 2 \sqrt{x - 2}$$

x - 2*sqrt(x - 2)

Detail solution

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

$1 - \frac{1}{\sqrt{x - 2}}$

The answer is:

$1 - \frac{1}{\sqrt{x - 2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        1    
1 - ---------
      _______
    \/ x - 2

$$1 - \frac{1}{\sqrt{x - 2}}$$

Simplify

The second derivative [src]

      1      
-------------
          3/2
2*(-2 + x)

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

Simplify

The third derivative [src]

     -3      
-------------
          5/2
4*(-2 + x)

$$- \frac{3}{4 \left(x - 2\right)^{\frac{5}{2}}}$$

Simplify

The graph

Derivative of y=x-2sqrt(x-2)