Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^x-1
Derivative of (-1)/x^3
Derivative of x^2/(x-1)
Derivative of 1/(2*x)
Identical expressions
one / six *ln*(-3x)
1 divide by 6 multiply by ln multiply by ( minus 3x)
one divide by six multiply by ln multiply by ( minus 3x)
1/6ln(-3x)
1/6ln-3x
1 divide by 6*ln*(-3x)
Similar expressions
1/6*ln*(3x)

The derivative of the function/ 1/6*ln*(-3x)

Derivative of 1/6ln(-3x)

The solution

You have entered [src]

log(-3*x)
---------
    6

$$\frac{\log{\left(- 3 x \right)}}{6}$$

log(-3*x)/6

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = - 3 x$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- 3 x\right)$ :
  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: $-3$
  The result of the chain rule is:
  
  $\frac{1}{x}$
So, the result is: $\frac{1}{6 x}$

The answer is:

$\frac{1}{6 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 1 
---
6*x

$$\frac{1}{6 x}$$

Simplify

The second derivative [src]

-1  
----
   2
6*x

$$- \frac{1}{6 x^{2}}$$

Simplify

The third derivative [src]

 1  
----
   3
3*x

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

Simplify