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Derivative of f(x)=log^0,5x-3

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  ____________
\/ log(x - 3) 
$$\sqrt{\log{\left(x - 3 \right)}}$$
sqrt(log(x - 3))
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
           1            
------------------------
            ____________
2*(x - 3)*\/ log(x - 3) 
$$\frac{1}{2 \left(x - 3\right) \sqrt{\log{\left(x - 3 \right)}}}$$
The second derivative [src]
     /         1     \     
    -|2 + -----------|     
     \    log(-3 + x)/     
---------------------------
          2   _____________
4*(-3 + x) *\/ log(-3 + x) 
$$- \frac{2 + \frac{1}{\log{\left(x - 3 \right)}}}{4 \left(x - 3\right)^{2} \sqrt{\log{\left(x - 3 \right)}}}$$
The third derivative [src]
          3               3       
1 + ------------- + --------------
    4*log(-3 + x)        2        
                    8*log (-3 + x)
----------------------------------
            3   _____________     
    (-3 + x) *\/ log(-3 + x)      
$$\frac{1 + \frac{3}{4 \log{\left(x - 3 \right)}} + \frac{3}{8 \log{\left(x - 3 \right)}^{2}}}{\left(x - 3\right)^{3} \sqrt{\log{\left(x - 3 \right)}}}$$