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

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
3 ______________
\/ log(5 - 2*x) 
$$\sqrt[3]{\log{\left(5 - 2 x \right)}}$$
log(5 - 2*x)^(1/3)
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. The derivative of the constant 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: goes to

          So, the result is:

        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]
            -2             
---------------------------
               2/3         
3*(5 - 2*x)*log   (5 - 2*x)
$$- \frac{2}{3 \left(5 - 2 x\right) \log{\left(5 - 2 x \right)}^{\frac{2}{3}}}$$
The second derivative [src]
       /         2      \    
    -4*|3 + ------------|    
       \    log(5 - 2*x)/    
-----------------------------
            2    2/3         
9*(-5 + 2*x) *log   (5 - 2*x)
$$- \frac{4 \left(3 + \frac{2}{\log{\left(5 - 2 x \right)}}\right)}{9 \left(2 x - 5\right)^{2} \log{\left(5 - 2 x \right)}^{\frac{2}{3}}}$$
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)   
$$\frac{16 \left(9 + \frac{9}{\log{\left(5 - 2 x \right)}} + \frac{5}{\log{\left(5 - 2 x \right)}^{2}}\right)}{27 \left(2 x - 5\right)^{3} \log{\left(5 - 2 x \right)}^{\frac{2}{3}}}$$