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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)
  • logx/log2*x3
  • log(x)/(log(2)*x³)
  • 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
log⁡(x)x3log⁡(2)\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:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}

    f(x)=log⁡(x)f{\left(x \right)} = \log{\left(x \right)} and g(x)=x3log⁡(2)g{\left(x \right)} = x^{3} \log{\left(2 \right)}.

    To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

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

    To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: x3x^{3} goes to 3x23 x^{2}

      So, the result is: 3x2log⁡(2)3 x^{2} \log{\left(2 \right)}

    Now plug in to the quotient rule:

    −3x2log⁡(2)log⁡(x)+x2log⁡(2)x6log⁡(2)2\frac{- 3 x^{2} \log{\left(2 \right)} \log{\left(x \right)} + x^{2} \log{\left(2 \right)}}{x^{6} \log{\left(2 \right)}^{2}}

  2. Now simplify:

    1−3log⁡(x)x4log⁡(2)\frac{1 - 3 \log{\left(x \right)}}{x^{4} \log{\left(2 \right)}}

The answer is:

1−3log⁡(x)x4log⁡(2)\frac{1 - 3 \log{\left(x \right)}}{x^{4} \log{\left(2 \right)}}

The graph
02468-8-6-4-2-1010200000-100000
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)
1x31log⁡(2)x−3log⁡(x)x4log⁡(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)
12log⁡(x)−7x5log⁡(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)
47−60log⁡(x)x6log⁡(2)\frac{47 - 60 \log{\left(x \right)}}{x^{6} \log{\left(2 \right)}}
Simplify
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