To find: The equation of the tangent line to the given equation at the point.
The equation of the tangent line to the curve at is .
The curve is .
The point is .
Derivative rules: Chain rule
If and are both differentiable function, then .
The equation of the tangent line at is, (1)
Where, m is the slope of the tangent line at and .
Consider the equation .
Differentiate the above equation implicitly with respect to x,
Differentiation with respect to x,
Let and apply the chain rule,
Combine the terms ,
Therefore, the derivative of y is .
The slope of the tangent line at is computed as follows,
Substitute the value ,
Thus, the slope of the tangent line at is .
Substitute for and in equation (1),
Therefore, the equation of the tangent line to the equation at is .
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