$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$

question 61

Multiple Choice

$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$ $x ^ { \frac { 6 } { 7 } } + y ^ { \frac { 8 } { 5 } } = 9$

• A)\(\frac { d y } { d x } = - \frac { 28 x ^ { \frac { - 1 } { 7 } } } { 15 y ^ { \frac { 3 } { 5 } } }\)
• B)\(\frac { d y } { d x } = - \frac { 15 x ^ { \frac { - 1 } { 7 } } } { 7 y ^ { \frac { 3 } { 5 } } }\)
• C)\(\frac { d y } { d x } = - \frac { 3 x ^ { \frac { - 1 } { 7 } } } { 28 y ^ { \frac { 3 } { 5 } } }\)
• D) \(\frac { d y } { d x } = \frac { 15 x ^ { \frac { - 1 } { 7 } } } { 28 y ^ { \frac { 3 } { 5 } } }\)
• E)\(\frac { d y } { d x } = - \frac { 15 x ^ { \frac { - 1 } { 7 } } } { 28 y ^ { \frac { 3 } { 5 } } }\)

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Definitions:

Volume Measurement

The process of determining the three-dimensional space occupied by a liquid, solid, or gas, using various instruments or formulas.

Calculated

Determined or deduced by mathematical methods or processes.

Directly Measured

Refers to values or quantities obtained through direct observation or instrumentation, without reliance on estimation or indirect calculation.

Total Lung Capacity

The maximum amount of air the lungs can hold, encompassing the vital capacity plus residual volume.