To find: The derivative by using implicit differentiation.
The implicit differentiation is .
The equation is .
(1) Chain rule: If and are both differentiable function, then
(2) Product Rule: If and are both differentiable, then
Let the independent variable be y and the dependent variable be x.
Differentiate implicitly with respect to y on both sides,
Apply the product rule,
Apply the chain rule (1),
Simplify further and obtain the derivative.
Therefore, the implicit differentiation is .
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