In Exercises 31–42, use implicit differentiation to find (a) the slope of the tangent line and (b) the equation of the tangent line at the indicated point on the graph. (Round answers to four decimal places as needed.) If only the x-coordinate is given, you must also find the y-coordinate. [HINT: See Example 2 and 3.]
To calculate: The slope of the tangent line to the graph of the equation at the point using the implicit differentiation.
The equation is and the point is .
Slope of tangent to the graph of at point is given by .
The derivative of function using the chain rule is
where, u is the function of x.
Constant multiple rule of derivative of function is where c is constant.
Consider the equation,
Find the slope of tangent line to the equation by determining the derivative.
Then, take of both sides of the equation,
Apply constant multiple rule,
Now, apply the chain rule and take the derivative of
To calculate: The equation of the tangent line to the graph of the equation at the point .
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