Derivative of 5-5ln(3x+4)

1. Differentiate $5 - 5 \log{\left(3 x + 4 \right)}$ term by term:

   1. The derivative of the constant $5$ is zero.

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

      1. Let $u = 3 x + 4$.

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

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

         1. Differentiate $3 x + 4$ term by term:

            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: $3$

            2. The derivative of the constant $4$ is zero.

            The result is: $3$

         The result of the chain rule is:

         $$\frac{3}{3 x + 4}$$

      So, the result is: $- \frac{15}{3 x + 4}$

   The result is: $- \frac{15}{3 x + 4}$

2. Now simplify:

   $$- \frac{15}{3 x + 4}$$

The answer is:

$$- \frac{15}{3 x + 4}$$