Derivative of -3x-5/(x-3)^2

1. Differentiate $- 3 x - \frac{5}{\left(x - 3\right)^{2}}$ 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 a constant times a function is the constant times the derivative of the function.

      1. Let $u = \left(x - 3\right)^{2}$.

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

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

         1. Let $u = x - 3$.

         2. Apply the power rule: $u^{2}$ goes to $2 u$

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

            1. Differentiate $x - 3$ term by term:

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

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

               The result is: $1$

            The result of the chain rule is:

            $$2 x - 6$$

         The result of the chain rule is:

         $$- \frac{2 x - 6}{\left(x - 3\right)^{4}}$$

      So, the result is: $\frac{5 \left(2 x - 6\right)}{\left(x - 3\right)^{4}}$

   The result is: $-3 + \frac{5 \left(2 x - 6\right)}{\left(x - 3\right)^{4}}$

2. Now simplify:

   $$\frac{10 x - 3 \left(x - 3\right)^{4} - 30}{\left(x - 3\right)^{4}}$$

The answer is:

$$\frac{10 x - 3 \left(x - 3\right)^{4} - 30}{\left(x - 3\right)^{4}}$$