Derivative of 7ln(x+5)-7x+10

1. Differentiate $\left(- 7 x + 7 \log{\left(x + 5 \right)}\right) + 10$ term by term:

   1. Differentiate $- 7 x + 7 \log{\left(x + 5 \right)}$ term by term:

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

         1. Let $u = x + 5$.

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

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

            1. Differentiate $x + 5$ term by term:

               1. Apply the power rule: $x$ goes to $1$

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

               The result is: $1$

            The result of the chain rule is:

            $$\frac{1}{x + 5}$$

         So, the result is: $\frac{7}{x + 5}$

      2. 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: $-7$

      The result is: $-7 + \frac{7}{x + 5}$

   2. The derivative of the constant $10$ is zero.

   The result is: $-7 + \frac{7}{x + 5}$

2. Now simplify:

   $$- \frac{7 x + 28}{x + 5}$$

The answer is:

$$- \frac{7 x + 28}{x + 5}$$