### Calculus: Finding Derivatives and Quotients#### Problem Statement**Given:**\[ f(x) = 4x + 1 \]\[ g(x) = 5x + 3 \]**Find the following.** *(You do not need to simplify your answers)*1. **The derivative of \( f(x) \) is \( f'(x) \) =** \[ \underline{\hspace{100px}} \]2. **The derivative of \( g(x) \) is \( g'(x) \) =** \[ \underline{\hspace{100px}} \]3. **The quotient of the derivatives is \( \frac{f'(x)}{g'(x)} \) =** \[ \underline{\hspace{100px}} \]4. **The quotient of \( f(x) \) and \( g(x) \) is \( \frac{f(x)}{g(x)} \) =** \[ \underline{\hspace{100px}} \]5. **The derivative of the quotient is \( \left( \frac{f(x)}{g(x)} \right)' \) =** \[ \underline{\hspace{100px}} \]**Which of the following is true:**- [ ] The derivative of \( f(x)g(x) \) is NOT \( \frac{f'(x)}{g'(x)} \)- [ ] The derivative of \( \frac{f(x)}{g(x)} \) IS \( \frac{f'(x)}{g'(x)} \)### ExplanationThe problem statement sets up functions \( f(x) \) and \( g(x) \) and asks for their derivatives, the quotient of these derivatives, the quotient of the functions themselves, and the derivative of the quotient. Finally, there are two statements that need to be evaluated as true or false.To solve these, apply the basic rules of differentiation and the quotient rule where necessary.

Name: ### Calculus: Finding Derivatives and Quotients#### Problem Statement
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: ### Calculus: Finding Derivatives and Quotients#### Problem Statement**Given:**\[ f(x) = 4x + 1 \]\[ g(x) = 5x + 3 \]**Find the following.** *(You do not need to simplify your answers)*1. **The derivative of \( f(x) \) is \( f'(x) \) =** \[ \und