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Derivative of:
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Graphing y =:
2*log(x)-x/2+1
Identical expressions
two *log(x)-x/ two + one
2 multiply by logarithm of (x) minus x divide by 2 plus 1
two multiply by logarithm of (x) minus x divide by two plus one
2log(x)-x/2+1
2logx-x/2+1
2*log(x)-x divide by 2+1
Similar expressions
2*log(x)-x/2-1
2*log(x)+x/2+1

The derivative of the function/ 2*log(x)-x/2+1

Derivative of 2*log(x)-x/2+1

The solution

You have entered [src]

           x    
2*log(x) - - + 1
           2

$$\left(- \frac{x}{2} + 2 \log{\left(x \right)}\right) + 1$$

2*log(x) - x/2 + 1

Detail solution

Differentiate $\left(- \frac{x}{2} + 2 \log{\left(x \right)}\right) + 1$ term by term:
1. Differentiate $- \frac{x}{2} + 2 \log{\left(x \right)}$ term by term:
  1. 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: $\frac{2}{x}$
  2. 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: $- \frac{1}{2}$
  The result is: $- \frac{1}{2} + \frac{2}{x}$
2. The derivative of the constant $1$ is zero.
The result is: $- \frac{1}{2} + \frac{2}{x}$
Now simplify:

$\frac{4 - x}{2 x}$

The answer is:

$\frac{4 - x}{2 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  1   2
- - + -
  2   x

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

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 2*log(x)-x/2+1