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Derivative of:
Derivative of sin(x)^2
Derivative of c
Derivative of x^4/log(x)
Derivative of log(x^2-6x+10)
Limit of the function:
x^4/log(x)
Identical expressions
x^ four /log(x)
x to the power of 4 divide by logarithm of (x)
x to the power of four divide by logarithm of (x)
x4/log(x)
x4/logx
x⁴/log(x)
x^4/logx
x^4 divide by log(x)

The derivative of the function/ x^4/log(x)

Derivative of x^4/log(x)

The solution

You have entered [src]

   4  
  x   
------
log(x)

$$\frac{x^{4}}{\log{\left(x \right)}}$$

  /   4  \
d |  x   |
--|------|
dx\log(x)/

$$\frac{d}{d x} \frac{x^{4}}{\log{\left(x \right)}}$$

Transform

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x^{4}$ and $g{\left(x \right)} = \log{\left(x \right)}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
Now plug in to the quotient rule:

$\frac{4 x^{3} \log{\left(x \right)} - x^{3}}{\log{\left(x \right)}^{2}}$
Now simplify:

$\frac{x^{3} \cdot \left(4 \log{\left(x \right)} - 1\right)}{\log{\left(x \right)}^{2}}$

The answer is:

$\frac{x^{3} \cdot \left(4 \log{\left(x \right)} - 1\right)}{\log{\left(x \right)}^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      3         3 
     x       4*x  
- ------- + ------
     2      log(x)
  log (x)

$$\frac{4 x^{3}}{\log{\left(x \right)}} - \frac{x^{3}}{\log{\left(x \right)}^{2}}$$

Simplify

The second derivative [src]

   /                    2   \
   |              1 + ------|
 2 |       8          log(x)|
x *|12 - ------ + ----------|
   \     log(x)     log(x)  /
-----------------------------
            log(x)

$$\frac{x^{2} \left(\frac{1 + \frac{2}{\log{\left(x \right)}}}{\log{\left(x \right)}} + 12 - \frac{8}{\log{\left(x \right)}}\right)}{\log{\left(x \right)}}$$

Simplify

The third derivative [src]

    /                    3         3                    \
    |              1 + ------ + -------     /      2   \|
    |                  log(x)      2      6*|1 + ------||
    |       18                  log (x)     \    log(x)/|
2*x*|12 - ------ - -------------------- + --------------|
    \     log(x)          log(x)              log(x)    /
---------------------------------------------------------
                          log(x)

$$\frac{2 x \left(\frac{6 \cdot \left(1 + \frac{2}{\log{\left(x \right)}}\right)}{\log{\left(x \right)}} - \frac{1 + \frac{3}{\log{\left(x \right)}} + \frac{3}{\log{\left(x \right)}^{2}}}{\log{\left(x \right)}} + 12 - \frac{18}{\log{\left(x \right)}}\right)}{\log{\left(x \right)}}$$

Simplify

The graph

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Identical expressions

Derivative of x^4/log(x)

The graph:

Piecewise:

The solution