Mister Exam

Other calculators


x*(log(x)/log(10))

Derivative of x*(log(x)/log(10))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   log(x)
x*-------
  log(10)
$$x \frac{\log{\left(x \right)}}{\log{\left(10 \right)}}$$
x*(log(x)/log(10))
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the product rule:

      ; to find :

      1. Apply the power rule: goes to

      ; to find :

      1. The derivative of is .

      The result is:

    To find :

    1. The derivative of the constant is zero.

    Now plug in to the quotient rule:


The answer is:

The graph
The first derivative [src]
   1       log(x)
------- + -------
log(10)   log(10)
$$\frac{\log{\left(x \right)}}{\log{\left(10 \right)}} + \frac{1}{\log{\left(10 \right)}}$$
The second derivative [src]
    1    
---------
x*log(10)
$$\frac{1}{x \log{\left(10 \right)}}$$
The third derivative [src]
   -1     
----------
 2        
x *log(10)
$$- \frac{1}{x^{2} \log{\left(10 \right)}}$$
The graph
Derivative of x*(log(x)/log(10))