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The derivative of the function/ x-2lnx

Derivative of x-2lnx

The solution

You have entered [src]

x - 2*log(x)

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

x - 2*log(x)

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    2
1 - -
    x

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

Simplify

The second derivative [src]

2 
--
 2
x

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

Simplify

The third derivative [src]

-4 
---
  3
 x

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

Simplify

The graph

Derivative of x-2lnx