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

Derivative of ln(1-3x)

The solution

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log(1 - 3*x)

$$\log{\left(1 - 3 x \right)}$$

d               
--(log(1 - 3*x))
dx

$$\frac{d}{d x} \log{\left(1 - 3 x \right)}$$

Transform

Detail solution

Let $u = 1 - 3 x$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(1 - 3 x\right)$ :
1. Differentiate $1 - 3 x$ term by term:
  1. The derivative of the constant $1$ 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: $x$ goes to $1$
      So, the result is: $3$
    So, the result is: $-3$
  The result is: $-3$
The result of the chain rule is:

$- \frac{3}{1 - 3 x}$
Now simplify:

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

The answer is:

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

The first derivative [src]

  -3   
-------
1 - 3*x

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

Simplify

The second derivative [src]

    -9     
-----------
          2
(-1 + 3*x)

$$- \frac{9}{\left(3 x - 1\right)^{2}}$$

Simplify

The third derivative [src]

     54    
-----------
          3
(-1 + 3*x)

$$\frac{54}{\left(3 x - 1\right)^{3}}$$

Simplify