The goal of this problem is to find dy/dx, where y and x satisfy the implicit eq

Question

The goal of this problem is to find dy/dx, where y and x satisfy the implicit equation x^2/64 + y^2/36 = 1 The steps in the process are: Implicitly differentiate both sides of the equation with respect to x Add or subtract terms from both sides of the resulting equation in order to collect all terms involving result will be an equation of the form A(x, y)dy/dx = B(x, y) where A(x, y) and B(x, y) each may depend on x, y, and constants Solve for dy/dx by dividing both sides of the equation by A(x, y). Now carry out steps 1 and 2 to find A(x, y) and B(x, y) A(x, y) = B(x, y) =

Explanation / Answer

x^2 /64 + y^2 /36 = 1

Differentiating with respect to x

2x/64 + (2y/36)(dy/dx) = 0

x/32 + (y/18)(dy/dx) = 0

dy/dx = (-x/32)(18/y)

dy/dx = -9x/16y

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