Derivative of (4x-3)⁵

1. Let $u = 4 x - 3$.

2. Apply the power rule: $u^{5}$ goes to $5 u^{4}$

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

   1. Differentiate $4 x - 3$ 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 $\left(-1\right) 3$ is zero.

      The result is: $4$

   The result of the chain rule is:

   $$20 \left(4 x - 3\right)^{4}$$

4. Now simplify:

   $$20 \left(4 x - 3\right)^{4}$$

The answer is:

$$20 \left(4 x - 3\right)^{4}$$