Mister Exam

Derivative of ln(2x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(2*x)
$$\log{\left(2 x \right)}$$
d           
--(log(2*x))
dx          
$$\frac{d}{d x} \log{\left(2 x \right)}$$
Detail solution
  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:


The answer is:

The graph
The first derivative [src]
1
-
x
$$\frac{1}{x}$$
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 ln(2x)