Derivative of sqrt4(x-1)^5

1. Let $u = \left(x - 1\right)^{0.25}$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 1\right)^{0.25}$:

   1. Let $u = x - 1$.

   2. Apply the power rule: $u^{0.25}$ goes to $\frac{0.25}{u^{0.75}}$

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

      1. Differentiate $x - 1$ term by term:

         1. Apply the power rule: $x$ goes to $1$

         2. The derivative of the constant $-1$ is zero.

         The result is: $1$

      The result of the chain rule is:

      $$\frac{0.25}{\left(x - 1\right)^{0.75}}$$

   The result of the chain rule is:

   $$1.25 \left(x - 1\right)^{0.25}$$

4. Now simplify:

   $$1.25 \left(x - 1\right)^{0.25}$$

The answer is: