Derivative of y=ln(2x+11)+5x

1. Differentiate $5 x + \log{\left(2 x + 11 \right)}$ term by term:

   1. Let $u = 2 x + 11$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x + 11\right)$:

      1. Differentiate $2 x + 11$ 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 $11$ is zero.

         The result is: $2$

      The result of the chain rule is:

      $$\frac{2}{2 x + 11}$$

   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: $5$

   The result is: $5 + \frac{2}{2 x + 11}$

2. Now simplify:

   $$\frac{10 x + 57}{2 x + 11}$$

The answer is:

$$\frac{10 x + 57}{2 x + 11}$$