Given Y = F(u) and U = G(x), Find Dy/dx $$y = \csc u , u = x ^ { 7 } + 10 x$$

question 388

Multiple Choice

Given y = f(u) and u = g(x) , find dy/dx = f(g(x) ) g(x) .
- $$y = \csc u , u = x ^ { 7 } + 10 x$$

• A) \(- \left( 7 x ^ { 6 } + 10 \right) \cot ^ { 2 } \left( x ^ { 7 } + 10 x \right)\)
• B) \(- \left( 7 x ^ { 6 } + 10 \right) \csc x \cot x\)
• C) \(- \csc \left( x ^ { 7 } + 10 x \right) \cot \left( x ^ { 7 } + 10 x \right)\)
• D) \(- \left( 7 x ^ { 6 } + 10 \right) \csc \left( x ^ { 7 } + 10 x \right) \cot \left( x ^ { 7 } + 10 x \right)\)

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Definitions:

Slaves

Individuals forced into servitude, denied personal freedom and rights, and compelled to work without pay.

1790

A year significant for the initiation of the first United States Census, marking a foundational aspect of the country's demographic record-keeping.

Shays's Rebellion

An armed uprising in western Massachusetts in 1786-1787, led by Daniel Shays, protesting economic injustices and seeking relief from debt and foreclosure.