Question

Consider the implicit equation 4xy²−6x²y−3x=0. Determine the derivative dy/dx at the point (1,−1)(1,−1).

A. dy/dx= -1/7
B dy/dx= -7/5
C dy/dx= 5/7
D. dy/dx= 7/5

Answer 1

To determine the derivative dy/dx at the point (1, -1) for the equation 4xy²-6x²y-3x=0, we employ implicit differentiation. The correct derivative is -7/5, which corresponds to option D.

Step-by-step explanation:

To find the derivative dy/dx of the implicit equation 4xy²-6x²y-3x=0 at the point (1, -1), we apply the implicit differentiation technique:

1. Differentiate both sides of the equation with respect to x, remembering to apply the product rule and chain rule where necessary.
2. Solve the resulting equation for dy/dx.
3. Substitute x=1 and y=-1 into the equation for dy/dx to find its value at that point.

By applying these steps, we find that the correct answer is dy/dx= -7/5, which corresponds to option D.

In the contribution, irrelevant data were provided and not used in the solving process.