Find the Partial Derivative $\frac { \partial z } { \partial y } \text { for the function } z = \cos \left( x ^ { 5 } + y ^ { 5 } \right)$

question 51

Multiple Choice

Find the partial derivative $\frac { \partial z } { \partial y } \text { for the function } z = \cos \left( x ^ { 5 } + y ^ { 5 } \right)$

• A) \(\frac { \partial z } { \partial y } = - 5 y ^ { 4 } \sin \left( x ^ { 5 } + y ^ { 5 } \right)\)
• B) \(\frac { \partial z } { \partial y } = - 5 y ^ { 6 } \sin \left( x ^ { 5 } + y ^ { 5 } \right)\)
• C) \(\frac { \partial z } { \partial y } = 5 y ^ { 6 } \sin \left( x ^ { 6 } + y ^ { 6 } \right)\)
• D) \(\frac { \partial z } { \partial y } = 5 y ^ { 6 } \cos \left( x ^ { 6 } + y ^ { 6 } \right)\)
• E) \(\frac { \partial z } { \partial y } = 5 y ^ { 4 } \cos \left( x ^ { 5 } + y ^ { 5 } \right)\)

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Definitions:

Body Sounds

Audible sounds made by the body, often used in medical diagnosis, such as heartbeats, intestinal noises, or breath sounds.

Vibrations

Oscillations or repetitive motions around an equilibrium point, which can occur in physical systems ranging from simple pendulums to complex structures like buildings and machinery.

Range Of Motion

The complete range of motion that a joint can achieve, typically involving both bending and straightening actions.

Manipulation

In a therapeutic context, manipulation involves the skillful handling, moving, or using of something or someone, often to achieve a desired outcome in physical therapy or psychology.