Question

Find dy/dx by implicit differentiation for the equation x sin(y) y sin(x) = 6.

Answer 1

To find dy/dx by implicit differentiation for the equation x sin(y) y sin(x) = 6, we need to differentiate both sides of the equation with respect to x using the product rule and chain rule.

Step-by-step explanation:

To find dy/dx by implicit differentiation for the equation x sin(y) y sin(x) = 6, we need to differentiate both sides of the equation with respect to x. Let's start by applying the product rule:

• Product rule: (u v)' = u' v + u v'
• Chain rule: (f(g(x)))' = f'(g(x)) · g'(x)

After using the product rule and the chain rule, we can simplify the equation and solve for dy/dx. The final result is:

dy/dx = -(x sin(y) + y sin(x))/(x cos(y) + y cos(x))