Derivative of 1/x+log(x)

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1         
- + log(x)
x

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

1/x + log(x)

Detail solution

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

$\frac{x - 1}{x^{2}}$

The answer is:

$\frac{x - 1}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1   1 
- - --
x    2
    x

$$\frac{1}{x} - \frac{1}{x^{2}}$$

Simplify

The second derivative [src]

     2
-1 + -
     x
------
   2  
  x

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

Simplify

The third derivative [src]

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

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

Simplify

The graph