Final Answer:
The derivative of the expression e^(9xy) * sin(xy) with respect to x using implicit differentiation involves both the product and chain rules.
Step-by-step explanation:
Given Function: Consider the function y = e^(9xy) * sin(xy).
Apply Implicit Differentiation: Differentiate both sides of the equation with respect to x using the product and chain rules.
Derivative of e^(9xy): Apply the chain rule to find the derivative of e^(9xy) with respect to x.
Derivative of sin(xy): Apply the chain rule to find the derivative of sin(xy) with respect to x.
Combine Results: Combine the derivatives obtained from the product and chain rules.
Final Answer: The final expression represents the derivative of the given function with respect to x.