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The derivative of the function/ log2x+1/2x

Derivative of log2x+1/2x

The solution

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           x
log(2*x) + -
           2

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

d /           x\
--|log(2*x) + -|
dx\           2/

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

Transform

Detail solution

Differentiate $\frac{x}{2} + \log{\left(2 x \right)}$ term by term:
1. Let $u = 2 x$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
  1. 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: $2$
  The result of the chain rule is:
  
  $\frac{1}{x}$
4. 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: $\frac{1}{2} + \frac{1}{x}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1   1
- + -
2   x

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

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

Derivative of log2x+1/2x