Mister Exam

# Derivative of ln(1-3x)

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

from to

### The solution

You have entered [src]
log(1 - 3*x)
$$\log{\left(1 - 3 x \right)}$$
d
--(log(1 - 3*x))
dx              
$$\frac{d}{d x} \log{\left(1 - 3 x \right)}$$
Detail solution
1. Let .

2. The derivative of is .

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

1. Differentiate term by term:

1. The derivative of the constant is zero.

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

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:

So, the result is:

The result is:

The result of the chain rule is:

4. Now simplify:

The first derivative [src]
  -3
-------
1 - 3*x
$$- \frac{3}{1 - 3 x}$$
The second derivative [src]
    -9
-----------
2
(-1 + 3*x) 
$$- \frac{9}{\left(3 x - 1\right)^{2}}$$
The third derivative [src]
     54
-----------
3
(-1 + 3*x) 
$$\frac{54}{\left(3 x - 1\right)^{3}}$$