Im am not getting any of the suggested answers, which is the correct answer and how? ### Differentiation ExerciseLet \( \alpha \), \( \beta \), and \( \gamma \) be real valued constants.Let \( f(x) = 3 \alpha x^4 \).Let \( g(x) = 2 \beta x^4 + \gamma \).Let \( h(x) = \sqrt{2x} \).Determine \( \frac{d}{dx} \left( \frac{f(x)}{h(x)} \right) \). Hint: Rewrite the quotient with fractional exponents and reduce first. Then factor out the constants so that you are left with a power function to differentiate.\[ \frac{d}{dx} \left( \frac{f(x)}{h(x)} \right) = \]Choose the correct option:- \( \bigcirc \) \( 12 \alpha x^3 \sqrt{2x} \)- \( \bigcirc \) \( \sqrt{2x} \left( \frac{4x^2 + 11 \alpha x}{2x} \right) \)- \( \bigcirc \) \( \sqrt{2x} \left( \frac{\alpha x^2}{2} \right) \)- \( \bigcirc \) \( \frac{21 \alpha x^2 \sqrt{x}}{2 \sqrt{2}} \)**Explanation:**To solve this, follow the hint provided. Initially, rewrite the quotient with fractional exponents and simplify. After that, factor out any constants so you have a power function left to differentiate.This problem tests your knowledge of:1. Quotient rule2. Simplifying expressions with fractional exponents3. Differentiating power functions

Name: Im am not getting any of the suggested answers, which is the correct a
Uploaded: 2024-03-20T07:07:50.000Z
Channel: Bartleby
Description: Im am not getting any of the suggested answers, which is the correct answer and how? ### Differentiation ExerciseLet \( \alpha \), \( \beta \), and \( \gamma \) be real valued constants.Let \( f(x) = 3 \alpha x^4 \).Let \( g(x) = 2 \beta x^4 + \gamma