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Derivative of:
Derivative of cos(x/3)
Derivative of √x
Derivative of xcos(x)
Derivative of (x^2-4)^3
Identical expressions
one /(two x- four)^ one /2
1 divide by (2x minus 4) to the power of 1 divide by 2
one divide by (two x minus four) to the power of one divide by 2
1/(2x-4)1/2
1/2x-41/2
1/2x-4^1/2
1 divide by (2x-4)^1 divide by 2
Similar expressions
1/(2x+4)^1/2

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

Derivative of 1/(2x-4)^1/2

The solution

You have entered [src]

     1     
-----------
  _________
\/ 2*x - 4

$$\frac{1}{\sqrt{2 x - 4}}$$

1/(sqrt(2*x - 4))

Detail solution

Let $u = \sqrt{2 x - 4}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{2 x - 4}$ :
1. Let $u = 2 x - 4$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x - 4\right)$ :
  1. Differentiate $2 x - 4$ term by term:
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $2$
    2. The derivative of the constant $-4$ is zero.
    The result is: $2$
  The result of the chain rule is:
  
  $\frac{1}{\sqrt{2 x - 4}}$
The result of the chain rule is:

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         -1          
---------------------
            _________
(2*x - 4)*\/ 2*x - 4

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

Simplify

The second derivative [src]

       ___   
   3*\/ 2    
-------------
          5/2
8*(-2 + x)

$$\frac{3 \sqrt{2}}{8 \left(x - 2\right)^{\frac{5}{2}}}$$

Simplify

The third derivative [src]

        ___   
  -15*\/ 2    
--------------
           7/2
16*(-2 + x)

$$- \frac{15 \sqrt{2}}{16 \left(x - 2\right)^{\frac{7}{2}}}$$

Simplify