Derivative of y=log(tan4-3x)

1. Let $u = - 3 x + \tan{\left(4 \right)}$.

2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$.

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- 3 x + \tan{\left(4 \right)}\right)$:

   1. Differentiate $- 3 x + \tan{\left(4 \right)}$ term by term:

      1. Rewrite the function to be differentiated:

         $$\tan{\left(4 \right)} = \frac{\sin{\left(4 \right)}}{\cos{\left(4 \right)}}$$

      2. The derivative of the constant $\frac{\sin{\left(4 \right)}}{\cos{\left(4 \right)}}$ is zero.

      3. 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:

   $$- \frac{3}{- 3 x + \tan{\left(4 \right)}}$$

4. Now simplify:

   $$\frac{3}{3 x - \tan{\left(4 \right)}}$$

The answer is:

$$\frac{3}{3 x - \tan{\left(4 \right)}}$$