Find the Requested Partial Derivative $( \partial \mathrm { w } / \partial \mathrm { z } ) _ { \mathrm { x } }$

question 373

Multiple Choice

Find the requested partial derivative.
- $( \partial \mathrm { w } / \partial \mathrm { z } ) _ { \mathrm { x } }$ at $( \mathrm { x } , \mathrm { y } , \mathrm { z } , \mathrm { w } ) = ( 1,2,9,302 )$ if $\mathrm { w } = \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } + 12 \mathrm { xyz }$ and $\mathrm { z } = \mathrm { x } ^ { 3 } + \mathrm { y } ^ { 3 }$

• A) \(\frac { 308 } { 3 }\)
• B) \(\frac { 154 } { 3 }\)
• C) 154
• D) 77

---

Definitions:

Module

In engineering, a measure of gear tooth size which is the ratio of the pitch diameter to the number of teeth, influencing the gear's size and interaction.

Cutting Data

Critical information related to machining processes, including but not limited to speeds, feeds, and depths of cut, used to optimize machining operations.

Gear Teeth

The individual protrusions on the rim of a gear that interlock with those on another gear to transmit torque and motion.

Diametral Pitch

A measure of the fineness of the gear teeth, expressed as the number of teeth per inch of the gear's diameter.