Mister Exam

Derivative of log2x+1/2x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
           x
log(2*x) + -
           2
$$\frac{x}{2} + \log{\left(2 x \right)}$$
d /           x\
--|log(2*x) + -|
dx\           2/
$$\frac{d}{d x} \left(\frac{x}{2} + \log{\left(2 x \right)}\right)$$
Detail solution
  1. Differentiate term by term:

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    4. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
1   1
- + -
2   x
$$\frac{1}{2} + \frac{1}{x}$$
The second derivative [src]
-1 
---
  2
 x 
$$- \frac{1}{x^{2}}$$
The third derivative [src]
2 
--
 3
x 
$$\frac{2}{x^{3}}$$
The graph
Derivative of log2x+1/2x