Derivative of y=ln(2x+5)+67x-3

1. Differentiate $\left(67 x + \log{\left(2 x + 5 \right)}\right) - 3$ term by term:

   1. Differentiate $67 x + \log{\left(2 x + 5 \right)}$ term by term:

      1. Let $u = 2 x + 5$.

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

      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x + 5\right)$:

         1. Differentiate $2 x + 5$ 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: $2$

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

            The result is: $2$

         The result of the chain rule is:

         $$\frac{2}{2 x + 5}$$

      4. 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: $67$

      The result is: $67 + \frac{2}{2 x + 5}$

   2. The derivative of the constant $-3$ is zero.

   The result is: $67 + \frac{2}{2 x + 5}$

2. Now simplify:

   $$\frac{134 x + 337}{2 x + 5}$$

The answer is:

$$\frac{134 x + 337}{2 x + 5}$$