To find: The derivative by the use of implicit differentiation.
The derivative of by the use of 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 y be an independent variable and x be a dependent variable.
The given equation is,
Differentiate implicitly with respect to y on both sides of the above equation,
Apply the product rule (2) and simplify the terms,
Apply the chain rule (1) as,
Combine the terms containing and obtain the expression for .
Therefore, the derivative of by the use of implicit differentiation is .
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