Find the Four Second Partial Derivatives $z = x ^ { 2 } + 8 x y + 6 y ^ { 2 }$

question 82

Multiple Choice

Find the four second partial derivatives. Observe that the second mixed partials are equal. $z = x ^ { 2 } + 8 x y + 6 y ^ { 2 }$

• A) \(\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 2 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 6 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 0\)
• B) \(\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 6 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 8\)
• C) \(\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 2 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 12 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 8\)
• D) \(\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 8\)
• E) \(\frac { \partial ^ { 2 } z } { \partial x ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial y ^ { 2 } } = 0 , \frac { \partial ^ { 2 } z } { \partial x \partial y } = \frac { \partial ^ { 2 } z } { \partial y \partial x } = 0\)

---

Definitions:

Creolization

The process in which different cultures come into contact and create new, blended cultural practices, languages, and identities.

Back-translation

A method used in the process of translating a document or text back into the original language by a different translator to ensure accuracy and consistency.

Cross-cultural Analysis

The examination of how cultural differences impact behavior, practices, and values across different societies or cultural groups.

Global Analysis

The comprehensive examination and evaluation of global markets, including trends, economic factors, and conditions that affect business operations and strategy on a worldwide scale.