Final answer:
To find dy/dx by implicit differentiation for the equation x sin(y) y sin(x) = 4, we can differentiate both sides of the equation and solve for dy/dx using the chain rule and product rule.
Step-by-step explanation:
The student is asking how to find dy/dx by implicit differentiation for the equation x sin(y) + y sin(x) = 4.
To perform implicit differentiation, we take the derivative of both sides of the equation with respect to x, remembering to apply the product rule and the chain rule as necessary. We will differentiate term by term.
The derivative of x sin(y) with respect to x is sin(y) + x cos(y) dy/dx. Similarly, the derivative of y sin(x) is sin(x) + y cos(x) dy/dx. After differentiation, we'll get an equation involving dy/dx, which we can then solve for dy/dx.