Question 1193312
**1. y = ln^3(x + sin(x))**

* **Chain Rule:** 
   * Let u = ln(x + sin(x)) 
   * Then y = u^3 
   * dy/du = 3u^2 
   * du/dx = 1 / (x + sin(x)) * (1 + cos(x)) 

* **Apply Chain Rule:**
   * dy/dx = dy/du * du/dx 
   * dy/dx = 3u^2 * (1 + cos(x)) / (x + sin(x)) 

* **Substitute back u:**
   * dy/dx = 3[ln(x + sin(x))]^2 * (1 + cos(x)) / (x + sin(x))

**2. y = tan^(-1)(3x)**

* **Chain Rule:**
   * Let u = 3x
   * Then y = tan^(-1)(u)
   * dy/du = 1 / (1 + u^2) 
   * du/dx = 3

* **Apply Chain Rule:**
   * dy/dx = dy/du * du/dx 
   * dy/dx = 1 / (1 + u^2) * 3 

* **Substitute back u:**
   * dy/dx = 3 / (1 + (3x)^2) 
   * dy/dx = 3 / (1 + 9x^2) 

I hope this helps! Let me know if you have any other questions.