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Identical expressions
- two log(two -x)^(one /2)
minus 2 logarithm of (2 minus x) to the power of (1 divide by 2)
minus two logarithm of (two minus x) to the power of (one divide by 2)
-2log(2-x)(1/2)
-2log2-x1/2
-2log2-x^1/2
-2log(2-x)^(1 divide by 2)
Similar expressions
-2log(2+x)^(1/2)
2log(2-x)^(1/2)

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

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

The solution

You have entered [src]

     ____________
-2*\/ log(2 - x)

$$- 2 \sqrt{\log{\left(2 - x \right)}}$$

-2*sqrt(log(2 - x))

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          1           
----------------------
          ____________
(2 - x)*\/ log(2 - x)

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

Simplify

The second derivative [src]

              1           
      2 + ----------      
          log(2 - x)      
--------------------------
          2   ____________
2*(-2 + x) *\/ log(2 - x)

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

Simplify

The third derivative [src]

   /         3               3      \
-2*|1 + ------------ + -------------|
   |    4*log(2 - x)        2       |
   \                   8*log (2 - x)/
-------------------------------------
               3   ____________      
       (-2 + x) *\/ log(2 - x)

$$- \frac{2 \left(1 + \frac{3}{4 \log{\left(2 - x \right)}} + \frac{3}{8 \log{\left(2 - x \right)}^{2}}\right)}{\left(x - 2\right)^{3} \sqrt{\log{\left(2 - x \right)}}}$$

Simplify

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

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The solution