Use Implicit Differentiation to Find an Equation of the Tangent $$y = \sin x y ^ { 6 } ; \quad \left( \frac { \pi } { 2 } , 1 \right)$$

question 33

Short Answer

Use implicit differentiation to find an equation of the tangent line to the curve at the indicated point.
$$y = \sin x y ^ { 6 } ; \quad \left( \frac { \pi } { 2 } , 1 \right)$$

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Definitions:

Equilibrium Price

The price at which the quantity of a good or service demanded equals the quantity supplied, leading to a stable market condition.

Marginal Cost

The expenditure required to produce an additional single unit of a product or service.

Total Revenue

The total amount of money generated by a business from selling its goods or services, calculated as the unit price multiplied by the quantity sold.

Competitive Industry

An industry where numerous producers are in competition with one another, leading to a situation where no single firm has significant market power, and prices are determined by overall supply and demand.