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y=log4(x+x^3)

Derivative of y=log4(x+x^3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /     3\
log\x + x /
-----------
   log(4)  
$$\frac{\log{\left(x^{3} + x \right)}}{\log{\left(4 \right)}}$$
  /   /     3\\
d |log\x + x /|
--|-----------|
dx\   log(4)  /
$$\frac{d}{d x} \frac{\log{\left(x^{3} + x \right)}}{\log{\left(4 \right)}}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
           2   
    1 + 3*x    
---------------
/     3\       
\x + x /*log(4)
$$\frac{3 x^{2} + 1}{\left(x^{3} + x\right) \log{\left(4 \right)}}$$
The second derivative [src]
              2
    /       2\ 
    \1 + 3*x / 
6 - -----------
     2 /     2\
    x *\1 + x /
---------------
/     2\       
\1 + x /*log(4)
$$\frac{6 - \frac{\left(3 x^{2} + 1\right)^{2}}{x^{2} \left(x^{2} + 1\right)}}{\left(x^{2} + 1\right) \log{\left(4 \right)}}$$
The third derivative [src]
  /                             3 \
  |      /       2\   /       2\  |
  |    9*\1 + 3*x /   \1 + 3*x /  |
2*|3 - ------------ + ------------|
  |            2                 2|
  |       1 + x        2 /     2\ |
  \                   x *\1 + x / /
-----------------------------------
           /     2\                
         x*\1 + x /*log(4)         
$$\frac{2 \cdot \left(3 - \frac{9 \cdot \left(3 x^{2} + 1\right)}{x^{2} + 1} + \frac{\left(3 x^{2} + 1\right)^{3}}{x^{2} \left(x^{2} + 1\right)^{2}}\right)}{x \left(x^{2} + 1\right) \log{\left(4 \right)}}$$
The graph
Derivative of y=log4(x+x^3)