Mister Exam

Lang:

The derivative of the function/ 1/2*lnx+3

Derivative of 1/2*lnx+3

The solution

You have entered [src]

log(x)    
------ + 3
  2

$$\frac{\log{\left(x \right)}}{2} + 3$$

log(x)/2 + 3

Detail solution

Differentiate $\frac{\log{\left(x \right)}}{2} + 3$ 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: $\frac{1}{2 x}$
2. The derivative of the constant $3$ is zero.
The result is: $\frac{1}{2 x}$

The answer is:

$\frac{1}{2 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 1 
---
2*x

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

Simplify

The second derivative [src]

-1  
----
   2
2*x

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

Simplify

The third derivative [src]

1 
--
 3
x

$$\frac{1}{x^{3}}$$

Simplify