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Graphing y =:
log(x^3-2*x)
Identical expressions
log(x^ three - two *x)
logarithm of (x cubed minus 2 multiply by x)
logarithm of (x to the power of three minus two multiply by x)
log(x3-2*x)
logx3-2*x
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log(x to the power of 3-2*x)
log(x^3-2x)
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logx^3-2x
Similar expressions
log(x^3+2*x)

The derivative of the function/ log(x^3-2*x)

Derivative of log(x^3-2*x)

The solution

You have entered [src]

   / 3      \
log\x  - 2*x/

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

d /   / 3      \\
--\log\x  - 2*x//
dx

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

Transform

Detail solution

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$\frac{3 x^{2} - 2}{x^{3} - 2 x}$$

Simplify

The second derivative [src]

               2
    /        2\ 
    \-2 + 3*x / 
6 - ------------
     2 /      2\
    x *\-2 + x /
----------------
          2     
    -2 + x

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

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Derivative of log(x^3-2*x)

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The solution