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  • Identical expressions

  • log(x)/(log(two)*x^ three)
  • logarithm of (x) divide by ( logarithm of (2) multiply by x cubed )
  • logarithm of (x) divide by ( logarithm of (two) multiply by x to the power of three)
  • log(x)/(log(2)*x3)
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  • log(x)/(log(2)*x to the power of 3)
  • log(x)/(log(2)x^3)
  • log(x)/(log(2)x3)
  • logx/log2x3
  • logx/log2x^3
  • log(x) divide by (log(2)*x^3)
The derivative of the function/ log(x)/(log(2)*x^3)

Derivative of log(x)/(log(2)*x^3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  log(x) 
---------
        3
log(2)*x
$$\frac{\log{\left(x \right)}}{x^{3} \log{\left(2 \right)}}$$ 
log(x)/((log(2)*x^3))
Detail solution

  1. Apply the quotient rule, which is:

    and .

    To find :

    1. The derivative of is .

    To find :

    1. 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:

    Now plug in to the quotient rule:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
/    1    \            
|---------|            
| 3       |            
\x *log(2)/    3*log(x)
----------- - ---------
     x         4       
              x *log(2)
$$\frac{\frac{1}{x^{3}} \frac{1}{\log{\left(2 \right)}}}{x} - \frac{3 \log{\left(x \right)}}{x^{4} \log{\left(2 \right)}}$$
Simplify
The second derivative [src] 
-7 + 12*log(x)
--------------
   5          
  x *log(2)
$$\frac{12 \log{\left(x \right)} - 7}{x^{5} \log{\left(2 \right)}}$$
Simplify
The third derivative [src] 
47 - 60*log(x)
--------------
   6          
  x *log(2)
$$\frac{47 - 60 \log{\left(x \right)}}{x^{6} \log{\left(2 \right)}}$$
Simplify
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