Find the Derivative Of $g(x)=\frac{x^{3 / 2}-6 x+x^{1 / 2}}{x^{3 / 2}}$

question 96

Multiple Choice

Find the derivative of $g(x) =\frac{x^{3 / 2}-6 x+x^{1 / 2}}{x^{3 / 2}}$
with respect to x.

• A) \(\frac{3}{x^{3 / 2}}+\frac{-1}{x^{2}}\)
• B) \(\frac{-48}{x^{3 / 2}}-\frac{-8.5}{x^{2}}\)
• C) \(\frac{1.5 x^{05}-6+1 / 2 x^{-1 / 2}}{1.5 x^{0.5}}\)
• D)6x - 3

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Definitions:

Ligament

A short band of tough, flexible, fibrous connective tissue that connects two bones or cartilages or holds together a joint.

Bronchoconstriction

A narrowing of the airways in the lungs due to the tightening of surrounding smooth muscle, leading to coughing, wheezing, and shortness of breath.

Airway Inflammation

The swelling and irritation of the air passages within the lungs, which can lead to symptoms such as coughing, wheezing, and shortness of breath.

Breathing Difficulty

Challenges or discomfort in inhaling or exhaling air, which can be a symptom of various health conditions.