Question

If (x)sin(2y) = (y)cos(2x), then what is dy over dx at the point pi over 4 comma pi over 2 question mark

Answer 1

To find dy/dx of the equation (x)sin(2y) = (y)cos(2x) at the point (pi/4, pi/2), one should differentiate implicitly, apply the product and chain rules, and then substitute the point's values to solve for dy/dx.

Step-by-step explanation:

The question involves finding the derivative dy/dx for the equation (x)sin(2y) = (y)cos(2x) at the point (pi/4, pi/2). To find this, we need to differentiate implicitly with respect to x. Applying the product rule to both sides and using trigonometric identities, where needed, then solving for dy/dx will yield the required derivative at the specific point.

Here's the step-by-step method:

1. Differentiate both sides of the equation with respect to x, applying the product rule and the chain rule.
2. Isolate dy/dx on one side of the resulting equation.
3. Substitute the given point into the equation to evaluate dy/dx at (x = pi/4, y = pi/2).

Keep in mind that some trigonometric simplifications may occur due to the specific values at the point of interest.