Derivative of (4*x-9)^7

1. Let $u = 4 x - 9$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(4 x - 9\right)$:

   1. Differentiate $4 x - 9$ 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: $4$

      2. The derivative of the constant $-9$ is zero.

      The result is: $4$

   The result of the chain rule is:

   $$28 \left(4 x - 9\right)^{6}$$

4. Now simplify:

   $$28 \left(4 x - 9\right)^{6}$$

The answer is:

$$28 \left(4 x - 9\right)^{6}$$