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Derivative of:
Derivative of 5x^3
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Identical expressions
lg(two x- five)^ one /2
lg(2x minus 5) to the power of 1 divide by 2
lg(two x minus five) to the power of one divide by 2
lg(2x-5)1/2
lg2x-51/2
lg2x-5^1/2
lg(2x-5)^1 divide by 2
Similar expressions
lg(2x+5)^1/2

The derivative of the function/ lg(2x-5)^1/2

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

The solution

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  ______________
\/ log(2*x - 5)

$$\sqrt{\log{\left(2 x - 5 \right)}}$$

sqrt(log(2*x - 5))

Detail solution

Let $u = \log{\left(2 x - 5 \right)}$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(2 x - 5 \right)}$ :
1. Let $u = 2 x - 5$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x - 5\right)$ :
  1. Differentiate $2 x - 5$ 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 $-5$ is zero.
    The result is: $2$
  The result of the chain rule is:
  
  $\frac{2}{2 x - 5}$
The result of the chain rule is:

$\frac{1}{\left(2 x - 5\right) \sqrt{\log{\left(2 x - 5 \right)}}}$
Now simplify:

$\frac{1}{\left(2 x - 5\right) \sqrt{\log{\left(2 x - 5 \right)}}}$

The answer is:

$\frac{1}{\left(2 x - 5\right) \sqrt{\log{\left(2 x - 5 \right)}}}$

The graph

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The first derivative [src]

            1             
--------------------------
            ______________
(2*x - 5)*\/ log(2*x - 5)

$$\frac{1}{\left(2 x - 5\right) \sqrt{\log{\left(2 x - 5 \right)}}}$$

Simplify

The second derivative [src]

     /          1      \     
    -|2 + -------------|     
     \    log(-5 + 2*x)/     
-----------------------------
          2   _______________
(-5 + 2*x) *\/ log(-5 + 2*x)

$$- \frac{2 + \frac{1}{\log{\left(2 x - 5 \right)}}}{\left(2 x - 5\right)^{2} \sqrt{\log{\left(2 x - 5 \right)}}}$$

Simplify

The third derivative [src]

          3                6      
8 + -------------- + -------------
       2             log(-5 + 2*x)
    log (-5 + 2*x)                
----------------------------------
            3   _______________   
  (-5 + 2*x) *\/ log(-5 + 2*x)

$$\frac{8 + \frac{6}{\log{\left(2 x - 5 \right)}} + \frac{3}{\log{\left(2 x - 5 \right)}^{2}}}{\left(2 x - 5\right)^{3} \sqrt{\log{\left(2 x - 5 \right)}}}$$

Simplify

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

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The solution