how do i sole. i am getting confused or maybe i am tired of the millions of calculs assignments i get weekly. either way please help me ### Analyzing Differential Equations on an Educational Platform#### Problem Statement:**Objective:** Express the relationship between a small change in \( x \) and the corresponding change in \( y \) in the form \( dy = f(x) \, dx \).Given the equation:\[ y = 9 \sqrt{x} - \frac{8}{x} \]#### Choices:1. \[\circ \quad dy = \left( \frac{9 \sqrt{x}}{2} - \frac{8}{x^2} \right) dx\]2. \[\circ \quad dy = \left( \frac{9}{2 \sqrt{x}} - \frac{8}{x^2} \right) dx\]3. \[\circ \quad dy = \left( \frac{9 \sqrt{x}}{2} - \frac{8}{x^2} \right) dx\]4. \[\circ \quad dy = \left( \frac{9}{2 \sqrt{x}} - \frac{8}{x^2} \right) dx\]### Steps to Derive \( dy \):1. **Differentiate \( y \) with respect to \( x \):** Given: \[ y = 9 \sqrt{x} - \frac{8}{x} \]2. **Apply the Differentiation Rules:** - The derivative of \( 9 \sqrt{x} \): \[ 9 \sqrt{x} = 9x^{\frac{1}{2}} \] \[ \frac{d}{dx} (9x^{\frac{1}{2}}) = 9 \cdot \frac{1}{2} x^{\frac{-1}{2}} = \frac{9}{2} x^{-\frac{1}{2}} = \frac{9}{2 \sqrt{x}} \] - The derivative of \( - \frac{8}{x} \): \[ -\frac{8}{x} = -8x^{-1} \] \[ \frac{d}{dx} (-8x^{-1}) = -8 \cdot (-1) x^{-2} = \frac{8}{x^2} \

Name: how do i sole. i am getting confused or maybe i am tired of the milli
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: how do i sole. i am getting confused or maybe i am tired of the millions of calculs assignments i get weekly. either way please help me ### Analyzing Differential Equations on an Educational Platform#### Problem Statement:**Objective:** Express the