Use Integration to Find a General Solution of the Differential $$\frac { d y } { d x } = x ^ { 10 } e ^ { x ^ { 11 } }$$

question 43

Multiple Choice

Use integration to find a general solution of the differential equation. $$\frac { d y } { d x } = x ^ { 10 } e ^ { x ^ { 11 } }$$

• A) \(y = \frac { 1 } { 10 } e ^ { x ^ { 11 } } + C\)
• B) \(y = \frac { 1 } { 11 } e ^ { x ^ { 11 } } + C\)
• C) \(y = \frac { x ^ { 11 } } { 11 } e ^ { x ^ { 11 } } + C\)
• D) \(y = 11 e ^ { x ^ { 11 } } + C\)
• E) \(y = 10 e ^ { x ^ { 11 } } + C\)

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Definitions:

Object Permanence

The understanding that objects continue to exist even when they cannot be seen, heard, or touched, a concept important in the cognitive development of infants.

Egocentrism

A cognitive bias characterized by the inability to differentiate between one's own perspective and another person's perspective.

Conservation

A principle in cognitive development where a child recognizes that quantity does not change with physical rearrangement.

Theory of Mind

The skill to recognize and assign mental states such as beliefs, intentions, desires, imaginings, and understanding to oneself and others, while also comprehending that others possess their own unique beliefs, desires, and intentions that may not align with one's personal views.