Mister Exam

Other calculators

1/lnx
The derivative of the function/ 1/lnx

Derivative of 1/lnx

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1   
------
log(x)
1log⁡(x)\frac{1}{\log{\left(x \right)}} 
1/log(x)
Detail solution

  1. Let u=log⁡(x)u = \log{\left(x \right)}.

  2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

  3. Then, apply the chain rule. Multiply by ddxlog⁡(x)\frac{d}{d x} \log{\left(x \right)}:

    1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

    The result of the chain rule is:

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

The answer is:

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

The graph
02468-8-6-4-2-1010-200100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   -1    
---------
     2   
x*log (x)
−1xlog⁡(x)2- \frac{1}{x \log{\left(x \right)}^{2}}
Simplify
The second derivative [src] 
      2   
1 + ------
    log(x)
----------
 2    2   
x *log (x)
1+2log⁡(x)x2log⁡(x)2\frac{1 + \frac{2}{\log{\left(x \right)}}}{x^{2} \log{\left(x \right)}^{2}}
Simplify
The third derivative [src] 
   /      3         3   \
-2*|1 + ------ + -------|
   |    log(x)      2   |
   \             log (x)/
-------------------------
         3    2          
        x *log (x)
−2(1+3log⁡(x)+3log⁡(x)2)x3log⁡(x)2- \frac{2 \left(1 + \frac{3}{\log{\left(x \right)}} + \frac{3}{\log{\left(x \right)}^{2}}\right)}{x^{3} \log{\left(x \right)}^{2}}
Simplify
The graph
Derivative of 1/lnx
    © Mister Exam – Calculator