Derivative of (5x+7)^20

1. Let $u = 5 x + 7$.

2. Apply the power rule: $u^{20}$ goes to $20 u^{19}$

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(5 x + 7\right)$:

   1. Differentiate $5 x + 7$ 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: $5$

      2. The derivative of the constant $7$ is zero.

      The result is: $5$

   The result of the chain rule is:

   $$100 \left(5 x + 7\right)^{19}$$

4. Now simplify:

   $$100 \left(5 x + 7\right)^{19}$$

The answer is:

$$100 \left(5 x + 7\right)^{19}$$