Derivative of 2+(2/((2*x+3)*log(10)))

1. Differentiate $2 + \frac{2}{\left(2 x + 3\right) \log{\left(10 \right)}}$ term by term:

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

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

      1. Let $u = \left(2 x + 3\right) \log{\left(10 \right)}$.

      2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$

      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x + 3\right) \log{\left(10 \right)}$:

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

            1. Differentiate $2 x + 3$ 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 $3$ is zero.

               The result is: $2$

            So, the result is: $2 \log{\left(10 \right)}$

         The result of the chain rule is:

         $$- \frac{2}{\left(2 x + 3\right)^{2} \log{\left(10 \right)}}$$

      So, the result is: $- \frac{4}{\left(2 x + 3\right)^{2} \log{\left(10 \right)}}$

   The result is: $- \frac{4}{\left(2 x + 3\right)^{2} \log{\left(10 \right)}}$

2. Now simplify:

   $$- \frac{4}{\left(2 x + 3\right)^{2} \log{\left(10 \right)}}$$

The answer is:

$$- \frac{4}{\left(2 x + 3\right)^{2} \log{\left(10 \right)}}$$