Final answer:
To solve the equation using implicit differentiation, differentiate both sides of the equation with respect to x using the product rule. Isolate dy/dx and simplify the equation to solve for dy/dx.
Step-by-step explanation:
To solve the equation using implicit differentiation, we will differentiate both sides of the equation with respect to x. Start by differentiating ycos(x²) with respect to x, using the product rule. The derivative of y with respect to x is dy/dx, and the derivative of cos(x²) is -2xsin(x²). On the right side, the derivative of xcos(y²) with respect to x is cos(y²) - 2xysin(y²)dy/dx. Now, isolate dy/dx and simplify the equation to solve for dy/dx.
So, dy/dx = (-2xsin(x²) - cos(y²)) / (xcos(y²) + 2xysin(y²))