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The derivative of the function/ ln^(x-2)x

Derivative of ln^(x-2)x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   x - 2   
log     (x)
log⁡(x)x−2\log{\left(x \right)}^{x - 2} 
log(x)^(x - 2)
Detail solution

  1. Don't know the steps in finding this derivative.

    But the derivative is

    (x−2)x−2(log⁡(x−2)+1)\left(x - 2\right)^{x - 2} \left(\log{\left(x - 2 \right)} + 1\right)

  2. Now simplify:

    (x−2)x−2(log⁡(x−2)+1)\left(x - 2\right)^{x - 2} \left(\log{\left(x - 2 \right)} + 1\right)

The answer is:

(x−2)x−2(log⁡(x−2)+1)\left(x - 2\right)^{x - 2} \left(\log{\left(x - 2 \right)} + 1\right)

The graph
02468-8-6-4-2-1010-10001000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   x - 2    / x - 2                \
log     (x)*|-------- + log(log(x))|
            \x*log(x)              /
(log⁡(log⁡(x))+x−2xlog⁡(x))log⁡(x)x−2\left(\log{\left(\log{\left(x \right)} \right)} + \frac{x - 2}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{x - 2}
Simplify
The second derivative [src] 
             /                                 -2 + x    -2 + x \
             |                        2   -2 + ------ + --------|
   -2 + x    |/ -2 + x               \           x      x*log(x)|
log      (x)*||-------- + log(log(x))|  - ----------------------|
             \\x*log(x)              /           x*log(x)       /
((log⁡(log⁡(x))+x−2xlog⁡(x))2−−2+x−2x+x−2xlog⁡(x)xlog⁡(x))log⁡(x)x−2\left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{x - 2}{x \log{\left(x \right)}}\right)^{2} - \frac{-2 + \frac{x - 2}{x} + \frac{x - 2}{x \log{\left(x \right)}}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{x - 2}
Simplify
The third derivative [src] 
             /                                   3      2*(-2 + x)   2*(-2 + x)   3*(-2 + x)                                                      \
             |                            -3 - ------ + ---------- + ---------- + ----------     / -2 + x               \ /     -2 + x    -2 + x \|
             |                        3        log(x)       x             2        x*log(x)    3*|-------- + log(log(x))|*|-2 + ------ + --------||
   -2 + x    |/ -2 + x               \                               x*log (x)                   \x*log(x)              / \       x      x*log(x)/|
log      (x)*||-------- + log(log(x))|  + -------------------------------------------------- - ---------------------------------------------------|
             |\x*log(x)              /                         2                                                     x*log(x)                     |
             \                                                x *log(x)                                                                           /
((log⁡(log⁡(x))+x−2xlog⁡(x))3−3(log⁡(log⁡(x))+x−2xlog⁡(x))(−2+x−2x+x−2xlog⁡(x))xlog⁡(x)+−3−3log⁡(x)+2(x−2)x+3(x−2)xlog⁡(x)+2(x−2)xlog⁡(x)2x2log⁡(x))log⁡(x)x−2\left(\left(\log{\left(\log{\left(x \right)} \right)} + \frac{x - 2}{x \log{\left(x \right)}}\right)^{3} - \frac{3 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{x - 2}{x \log{\left(x \right)}}\right) \left(-2 + \frac{x - 2}{x} + \frac{x - 2}{x \log{\left(x \right)}}\right)}{x \log{\left(x \right)}} + \frac{-3 - \frac{3}{\log{\left(x \right)}} + \frac{2 \left(x - 2\right)}{x} + \frac{3 \left(x - 2\right)}{x \log{\left(x \right)}} + \frac{2 \left(x - 2\right)}{x \log{\left(x \right)}^{2}}}{x^{2} \log{\left(x \right)}}\right) \log{\left(x \right)}^{x - 2}
Simplify
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