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Identical expressions
y=log(x^ three + one)
y equally logarithm of (x cubed plus 1)
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y=log(x3+1)
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y=logx^3+1
Similar expressions
y=log(x^3-1)

The derivative of the function/ y=log(x^3+1)

Derivative of y=log(x^3+1)

The solution

You have entered [src]

   / 3    \
log\x  + 1/

$$\log{\left(x^{3} + 1 \right)}$$

log(x^3 + 1)

Detail solution

Let $u = x^{3} + 1$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{3} + 1\right)$ :
1. Differentiate $x^{3} + 1$ term by term:
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  2. The derivative of the constant $1$ is zero.
  The result is: $3 x^{2}$
The result of the chain rule is:

$\frac{3 x^{2}}{x^{3} + 1}$
Now simplify:

$\frac{3 x^{2}}{x^{3} + 1}$

The answer is:

$\frac{3 x^{2}}{x^{3} + 1}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    2 
 3*x  
------
 3    
x  + 1

$$\frac{3 x^{2}}{x^{3} + 1}$$

Simplify

The second derivative [src]

    /        3 \
    |     3*x  |
3*x*|2 - ------|
    |         3|
    \    1 + x /
----------------
          3     
     1 + x

$$\frac{3 x \left(- \frac{3 x^{3}}{x^{3} + 1} + 2\right)}{x^{3} + 1}$$

Simplify

The third derivative [src]

  /        3          6  \
  |     9*x        9*x   |
6*|1 - ------ + ---------|
  |         3           2|
  |    1 + x    /     3\ |
  \             \1 + x / /
--------------------------
               3          
          1 + x

$$\frac{6 \left(\frac{9 x^{6}}{\left(x^{3} + 1\right)^{2}} - \frac{9 x^{3}}{x^{3} + 1} + 1\right)}{x^{3} + 1}$$

Simplify

The graph

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Derivative of y=log(x^3+1)

The graph:

Piecewise:

The solution