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Derivative of 3/x-ln(x)/ln(10)

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3    log(x)
- - -------
x   log(10)

$$- \frac{\log{\left(x \right)}}{\log{\left(10 \right)}} + \frac{3}{x}$$

3/x - log(x)/log(10)

Detail solution

Differentiate $- \frac{\log{\left(x \right)}}{\log{\left(10 \right)}} + \frac{3}{x}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
  So, the result is: $- \frac{3}{x^{2}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  So, the result is: $- \frac{1}{x \log{\left(10 \right)}}$
The result is: $- \frac{1}{x \log{\left(10 \right)}} - \frac{3}{x^{2}}$
Now simplify:

$- \frac{x + \log{\left(1000 \right)}}{x^{2} \log{\left(10 \right)}}$

The answer is:

$- \frac{x + \log{\left(1000 \right)}}{x^{2} \log{\left(10 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  3        1    
- -- - ---------
   2   x*log(10)
  x

$$- \frac{1}{x \log{\left(10 \right)}} - \frac{3}{x^{2}}$$

Simplify

The second derivative [src]

   1      6
------- + -
log(10)   x
-----------
      2    
     x

$$\frac{\frac{1}{\log{\left(10 \right)}} + \frac{6}{x}}{x^{2}}$$

Simplify

The third derivative [src]

   /   1      9\
-2*|------- + -|
   \log(10)   x/
----------------
        3       
       x

$$- \frac{2 \left(\frac{1}{\log{\left(10 \right)}} + \frac{9}{x}\right)}{x^{3}}$$

Simplify