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Identical expressions
ln(five - two *x)^ one / three
ln(5 minus 2 multiply by x) to the power of 1 divide by 3
ln(five minus two multiply by x) to the power of one divide by three
ln(5-2*x)1/3
ln5-2*x1/3
ln(5-2x)^1/3
ln(5-2x)1/3
ln5-2x1/3
ln5-2x^1/3
ln(5-2*x)^1 divide by 3
Similar expressions
ln(5+2*x)^1/3

The derivative of the function/ ln(5-2*x)^1/3

Derivative of ln(5-2*x)^1/3

The solution

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

$$\sqrt[3]{\log{\left(5 - 2 x \right)}}$$

log(5 - 2*x)^(1/3)

Detail solution

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

$- \frac{2}{3 \left(5 - 2 x\right) \log{\left(5 - 2 x \right)}^{\frac{2}{3}}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            -2             
---------------------------
               2/3         
3*(5 - 2*x)*log   (5 - 2*x)

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

Simplify

The second derivative [src]

       /         2      \    
    -4*|3 + ------------|    
       \    log(5 - 2*x)/    
-----------------------------
            2    2/3         
9*(-5 + 2*x) *log   (5 - 2*x)

$$- \frac{4 \left(3 + \frac{2}{\log{\left(5 - 2 x \right)}}\right)}{9 \left(2 x - 5\right)^{2} \log{\left(5 - 2 x \right)}^{\frac{2}{3}}}$$

Simplify

The third derivative [src]

   /          5              9      \
16*|9 + ------------- + ------------|
   |       2            log(5 - 2*x)|
   \    log (5 - 2*x)               /
-------------------------------------
                 3    2/3            
    27*(-5 + 2*x) *log   (5 - 2*x)

$$\frac{16 \left(9 + \frac{9}{\log{\left(5 - 2 x \right)}} + \frac{5}{\log{\left(5 - 2 x \right)}^{2}}\right)}{27 \left(2 x - 5\right)^{3} \log{\left(5 - 2 x \right)}^{\frac{2}{3}}}$$

Simplify

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Derivative of ln(5-2*x)^1/3

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The solution