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

Derivative of log(x^4+x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   / 4    \
log\x  + x/
$$\log{\left(x^{4} + x \right)}$$
Transform
Detail solution

  1. Let .

  2. The derivative of is .

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. Apply the power rule: goes to

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       3
1 + 4*x 
--------
  4     
 x  + x
$$\frac{4 x^{3} + 1}{x^{4} + x}$$
Simplify
The second derivative [src] 
                 2
       /       3\ 
       \1 + 4*x / 
12*x - -----------
        2 /     3\
       x *\1 + x /
------------------
           3      
      1 + x
$$\frac{12 x - \frac{\left(4 x^{3} + 1\right)^{2}}{x^{2} \left(x^{3} + 1\right)}}{x^{3} + 1}$$
Simplify
The third derivative [src] 
  /                               3 \
  |        /       3\   /       3\  |
  |     18*\1 + 4*x /   \1 + 4*x /  |
2*|12 - ------------- + ------------|
  |              3                 2|
  |         1 + x        3 /     3\ |
  \                     x *\1 + x / /
-------------------------------------
                     3               
                1 + x
$$\frac{2 \left(12 - \frac{18 \left(4 x^{3} + 1\right)}{x^{3} + 1} + \frac{\left(4 x^{3} + 1\right)^{3}}{x^{3} \left(x^{3} + 1\right)^{2}}\right)}{x^{3} + 1}$$
Simplify
The graph
Derivative of log(x^4+x)
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