**Title: Calculating the Derivative of a Rational Function****Objective:**- Find the derivative \( f'(x) \) for the given function- Evaluate \( f'(x) \) at the specified point**Given Function:**\[ g(x) = \frac{5}{x - 3} \]**Task:**- Compute the derivative \( g'(x) \)- Evaluate \( g'(x) \) at \( x = 4 \)**Instructions:**1. **Identify the Type of Function:** - This is a rational function, specifically of the form \( \frac{c}{x - a} \).2. **Apply the Derivative Rule for Rational Functions:** - Recall that the derivative of \( \frac{c}{x} \) is \( -\frac{c}{x^2} \). - Use the chain rule if necessary for specific transformations of the denominator.3. **Calculation Steps:** a. **Find the Derivative \( g'(x) \):** - First, express \( g(x) \) in terms of a negative exponent: \[ g(x) = 5(x - 3)^{-1} \] - Differentiate using the power rule and chain rule: \[ g'(x) = -5(x - 3)^{-2} \cdot 1 \] \[ g'(x) = -\frac{5}{(x - 3)^2} \] b. **Evaluate \( g'(4) \):** - Substitute \( x = 4 \) into \( g'(x) \): \[ g'(4) = -\frac{5}{(4 - 3)^2} \] \[ g'(4) = -\frac{5}{1} \] \[ g'(4) = -5 \]**Conclusion:**The derivative \( g'(x) \) is \( -\frac{5}{(x - 3)^2} \) and the value of the derivative at \( x = 4 \) is \( -5 \).

Name: **Title: Calculating the Derivative of a Rational Function****Objecti
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: **Title: Calculating the Derivative of a Rational Function****Objective:**- Find the derivative \( f'(x) \) for the given function- Evaluate \( f'(x) \) at the specified point**Given Function:**\[ g(x) = \frac{5}{x - 3} \]**Task:**- Compute the deri