Derivative of (3x+5)^4

1. Let $u = 3 x + 5$.

2. Apply the power rule: $u^{4}$ goes to $4 u^{3}$

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

   1. Differentiate $3 x + 5$ 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 the constant $5$ is zero.

      The result is: $3$

   The result of the chain rule is:

   $$12 \left(3 x + 5\right)^{3}$$

4. Now simplify:

   $$12 \left(3 x + 5\right)^{3}$$

The answer is:

$$12 \left(3 x + 5\right)^{3}$$