Find the Rate of Change of the Distance Between the Origin

question 43

Multiple Choice

Find the rate of change of the distance between the origin and a moving point on the graph of $y = x ^ { 2 } + 7$ if $\frac { d x } { d t } = 6$ centimeters per second.

• A) \(\frac { d D } { d t } = \frac { 12 x ^ { 3 } + 90 x } { \sqrt { x ^ { 4 } + 15 x ^ { 2 } + 49 } }\)
• B) \(\frac { d D } { d t } = \frac { 6 x ^ { 3 } - 20 x } { x ^ { 3 } + 15 x ^ { 2 } + 49 }\)
• C) \(\frac { d D } { d t } = \frac { 12 x ^ { 3 } - 90 x } { \sqrt { x ^ { 3 } + 15 x ^ { 2 } + 49 } }\)
• D)\(\frac { d D } { d t } = \frac { 6 x ^ { 3 } + 90 x } { \sqrt { x ^ { 4 } + 14 x ^ { 2 } + 49 } }\)
• E)\(\frac { d D } { d t } = \frac { 12 x ^ { 3 } + 20 x } { x ^ { 4 } + 12 x ^ { 2 } + 49 }\)

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The capability to fulfill all of one's needs without external assistance, often in terms of producing food, goods, and services independently.

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A group of 19th-century American writers and philosophers who believed in the inherent goodness of both people and nature, emphasizing individual conscience and intuition.

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