Derivative of (x^2-3x)^5

1. Let $u = x^{2} - 3 x$.

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

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

   1. Differentiate $x^{2} - 3 x$ term by term:

      1. Apply the power rule: $x^{2}$ goes to $2 x$

      2. The derivative of a constant times a function is the constant times the derivative of the function.

         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: $3$

         So, the result is: $-3$

      The result is: $2 x - 3$

   The result of the chain rule is:

   $$5 \cdot \left(2 x - 3\right) \left(x^{2} - 3 x\right)^{4}$$

4. Now simplify:

   $$x^{4} \left(x - 3\right)^{4} \cdot \left(10 x - 15\right)$$

The answer is: