Mister Exam

Lang:

The derivative of the function/ log(5*x)

Derivative of log(5*x)

The solution

You have entered [src]

log(5*x)

$$\log{\left(5 x \right)}$$

log(5*x)

Detail solution

Let $u = 5 x$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x$ :
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: $5$
The result of the chain rule is:

$\frac{1}{x}$

The answer is:

$\frac{1}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1
-
x

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

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 log(5*x)