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Similar expressions
3/(x^3)-ln2x+7
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The derivative of the function/ 3/(x^3)+ln2x+7

Derivative of 3/(x^3)+ln2x+7

The solution

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3                
-- + log(2*x) + 7
 3               
x

$$\left(\log{\left(2 x \right)} + \frac{3}{x^{3}}\right) + 7$$

3/x^3 + log(2*x) + 7

Detail solution

Differentiate $\left(\log{\left(2 x \right)} + \frac{3}{x^{3}}\right) + 7$ term by term:
1. Differentiate $\log{\left(2 x \right)} + \frac{3}{x^{3}}$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Let $u = x^{3}$ .
    2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{3}$ :
      1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
      The result of the chain rule is:
      
      $- \frac{3}{x^{4}}$
    So, the result is: $- \frac{9}{x^{4}}$
  2. Let $u = 2 x$ .
  3. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
  4. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
    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: $2$
    The result of the chain rule is:
    
    $\frac{1}{x}$
  The result is: $\frac{1}{x} - \frac{9}{x^{4}}$
2. The derivative of the constant $7$ is zero.
The result is: $\frac{1}{x} - \frac{9}{x^{4}}$
Now simplify:

$\frac{x^{3} - 9}{x^{4}}$

The answer is:

$\frac{x^{3} - 9}{x^{4}}$

The graph

Plot the graph f(x)

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The first derivative [src]

1   9 
- - --
x    4
    x

$$\frac{1}{x} - \frac{9}{x^{4}}$$

Simplify

The second derivative [src]

     36
-1 + --
      3
     x 
-------
    2  
   x

$$\frac{-1 + \frac{36}{x^{3}}}{x^{2}}$$

Simplify

The third derivative [src]

  /    90\
2*|1 - --|
  |     3|
  \    x /
----------
     3    
    x

$$\frac{2 \left(1 - \frac{90}{x^{3}}\right)}{x^{3}}$$

Simplify