Derivative of (5x-2)^3

1. Let $u = 5 x - 2$.

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

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

   1. Differentiate $5 x - 2$ 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: $5$

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

      The result is: $5$

   The result of the chain rule is:

   $$15 \left(5 x - 2\right)^{2}$$

4. Now simplify:

   $$15 \left(5 x - 2\right)^{2}$$

The answer is:

$$15 \left(5 x - 2\right)^{2}$$