Derivative of ln(x)+x

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log(x) + x

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

d             
--(log(x) + x)
dx

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

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Detail solution

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

$\frac{x + 1}{x}$

The answer is:

$\frac{x + 1}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    1
1 + -
    x

$$1 + \frac{1}{x}$$

Simplify

The second derivative [src]

-1 
---
  2
 x

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

Simplify

The third derivative [src]

2 
--
 3
x

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

Simplify

The graph