Let H(x, Y) = $\frac { 3 x y } { x ^ { 2 } - y }$

question 50

Multiple Choice

Let H(x, y) = $\frac { 3 x y } { x ^ { 2 } - y }$ . Find $\frac { \partial ^ { 2 } \mathrm { H } } { \partial \mathrm { y } ^ { 2 } }$ .

• A) \(\frac { 6 x ^ { 3 } } { \left( x ^ { 2 } - y \right) ^ { 3 } }\)
• B) \(\frac { 6 x ^ { 3 } y - 6 x ^ { 5 } } { \left( x ^ { 2 } - y \right) ^ { 4 } }\)
• C) \(\frac { 3 x ^ { 3 } } { \left( x ^ { 2 } - y \right) ^ { 2 } }\)
• D) \(\frac { 9 x ^ { 4 } - 6 x ^ { 3 } - 9 x ^ { 2 } y } { \left( x ^ { 2 } - y \right) ^ { 3 } }\)
• E) none of these

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Definitions:

Vitamin Deficiency

Vitamin deficiency occurs when there is an insufficient intake or absorption of vitamins, leading to various health disorders and diseases.

Water-Soluble Vitamin

Vitamin, such as B complex and C, that is absorbed with water from the intestinal tract.

Vitamin C

An essential nutrient known for its antioxidant properties and role in collagen synthesis.

Acid-Base Balance

The regulation of the pH levels in bodily fluids, crucial for the body's overall functioning.