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Derivative of lg(2x-5)^1/2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  ______________
\/ log(2*x - 5) 
$$\sqrt{\log{\left(2 x - 5 \right)}}$$
sqrt(log(2*x - 5))
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. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        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 - 5)*\/ log(2*x - 5) 
$$\frac{1}{\left(2 x - 5\right) \sqrt{\log{\left(2 x - 5 \right)}}}$$
The second derivative [src]
     /          1      \     
    -|2 + -------------|     
     \    log(-5 + 2*x)/     
-----------------------------
          2   _______________
(-5 + 2*x) *\/ log(-5 + 2*x) 
$$- \frac{2 + \frac{1}{\log{\left(2 x - 5 \right)}}}{\left(2 x - 5\right)^{2} \sqrt{\log{\left(2 x - 5 \right)}}}$$
The third derivative [src]
          3                6      
8 + -------------- + -------------
       2             log(-5 + 2*x)
    log (-5 + 2*x)                
----------------------------------
            3   _______________   
  (-5 + 2*x) *\/ log(-5 + 2*x)    
$$\frac{8 + \frac{6}{\log{\left(2 x - 5 \right)}} + \frac{3}{\log{\left(2 x - 5 \right)}^{2}}}{\left(2 x - 5\right)^{3} \sqrt{\log{\left(2 x - 5 \right)}}}$$