Derivative of 7/(5-x)^2

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

   1. Let $u = \left(5 - x\right)^{2}$.

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

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

      1. Let $u = 5 - x$.

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

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

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

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

            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: $-1$

            The result is: $-1$

         The result of the chain rule is:

         $$2 x - 10$$

      The result of the chain rule is:

      $$- \frac{2 x - 10}{\left(5 - x\right)^{4}}$$

   So, the result is: $- \frac{7 \left(2 x - 10\right)}{\left(5 - x\right)^{4}}$

2. Now simplify:

   $$\frac{14}{\left(5 - x\right)^{3}}$$

The answer is:

$$\frac{14}{\left(5 - x\right)^{3}}$$