Derivative of y=sin³5x

1. Let $u = \sin{\left(x \right)}$.

2. Apply the power rule: $u^{35}$ goes to $35 u^{34}$

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

   1. The derivative of sine is cosine:

      $$\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$$

   The result of the chain rule is:

   $$35 \sin^{34}{\left(x \right)} \cos{\left(x \right)}$$

The answer is:

$$35 \sin^{34}{\left(x \right)} \cos{\left(x \right)}$$