Question

The value of $\vec{\nabla}\left(\frac{f}{g}\right)$ at points where $g(x) \neq 0$ is given by

• A. $f \vec{\nabla} g - g \vec{\nabla} f$
• B. $\frac{g \vec{\nabla} f - f \vec{\nabla} g}{g^2}$
• C. $\frac{f \vec{\nabla} g - g \vec{\nabla} f}{g^2}$
• D. $g \vec{\nabla} f - f \vec{\nabla} g$

Hint:

Vector differential operators ($\vec{\nabla}$) mirror single-variable calculus rules: - Product Rule: $\vec{\nabla}(f g) = f \vec{\nabla} g + g \vec{\nabla} f$ - Quotient Rule: $\vec{\nabla}(f/g) = \frac{g \vec{\nabla} f - f \vec{\nabla} g}{g^2}$

Answer 1

The Correct Option is B