Final answer:
To find dy/dx using implicit differentiation, differentiate both sides of the equation. Apply the chain rule and rearrange the equation to solve for dy/dx.
Step-by-step explanation:
To determine dy/dx using implicit differentiation for the equation 3sin(xy) + 4cos(xy) = 5, we will differentiate both sides of the equation with respect to x.
Starting with the left side of the equation, we apply the chain rule by differentiating sin(xy) with respect to x, yielding cos(xy) * (y + xy') + sin(xy) * (xy' + y') = 0.
On the right side, the derivative of a constant (5) is zero. Rearranging the equation and solving for dy/dx, we get dy/dx = -(cos(xy) * (y + xy') + sin(xy) * (xy' + y')) / (3cos(xy) + 4sin(xy)).