Derivative of (3x-1)^7

1. Let $u = 3 x - 1$.

2. Apply the power rule: $u^{7}$ goes to $7 u^{6}$

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x - 1\right)$:

   1. Differentiate $3 x - 1$ 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 $\left(-1\right) 1$ is zero.

      The result is: $3$

   The result of the chain rule is:

   $$21 \left(3 x - 1\right)^{6}$$

4. Now simplify:

   $$21 \left(3 x - 1\right)^{6}$$

The answer is:

$$21 \left(3 x - 1\right)^{6}$$