Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (x^2-1)/((2*x))
Derivative of sin(pi/2)
Derivative of sin(2*x)/cos(5*x)
Derivative of log(x)/x^4
Limit of the function:
log(x)/x^4
Identical expressions
log(x)/x^ four
logarithm of (x) divide by x to the power of 4
logarithm of (x) divide by x to the power of four
log(x)/x4
logx/x4
log(x)/x⁴
logx/x^4
log(x) divide by x^4

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

Derivative of log(x)/x^4

The solution

You have entered [src]

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

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

log(x)/x^4

Detail solution

Apply the quotient rule, which is:

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

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

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

$\frac{- 4 x^{3} \log{\left(x \right)} + x^{3}}{x^{8}}$
Now simplify:

$\frac{1 - 4 \log{\left(x \right)}}{x^{5}}$

The answer is:

$\frac{1 - 4 \log{\left(x \right)}}{x^{5}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 1     4*log(x)
---- - --------
   4       5   
x*x       x

$$\frac{1}{x x^{4}} - \frac{4 \log{\left(x \right)}}{x^{5}}$$

Simplify

The second derivative [src]

-9 + 20*log(x)
--------------
       6      
      x

$$\frac{20 \log{\left(x \right)} - 9}{x^{6}}$$

Simplify

The third derivative [src]

2*(37 - 60*log(x))
------------------
         7        
        x

$$\frac{2 \left(37 - 60 \log{\left(x \right)}\right)}{x^{7}}$$

Simplify

The graph

Derivative of log(x)/x^4