To find: The equation of the tangent line to the given equation at the point.
The equation of the tangent line to the equation at the point is .
The curve is .
The point is .
(1) Chain rule: If and are both differentiable function, then .
(2) Product rule:
The equation of the tangent line at is, (1)
Where, m is the slope of the tangent line at and .
Obtain the equation of the tangent line to the equation at the point.
Rewrite the given equation as follows,
Differentiate the equation implicitly with respect to x,
Apply the chain rule (1) and simplify the terms,
Substitute for ,
Thus, the slope of the tangent at is .
Substitute for and in equation (1),
Therefore, the equation of the tangent line to the equation at is .
The graph of the given curve and tangent line is shown below Figure 1.
From Figure 1, it is observed that the line is tangent to the equation at the point .
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