Derivative of y=(15-3x)¹⁰¹

1. Let $u = 15 - 3 x$.

2. Apply the power rule: $u^{10}$ goes to $10 u^{9}$

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(15 - 3 x\right)$:

   1. Differentiate $15 - 3 x$ term by term:

      1. The derivative of the constant $15$ is zero.

      2. 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: $-3$

      The result is: $-3$

   The result of the chain rule is:

   $$- 30 \left(15 - 3 x\right)^{9}$$

4. Now simplify:

   $$590490 \left(x - 5\right)^{9}$$

The answer is:

$$590490 \left(x - 5\right)^{9}$$