Final answer:
To find dy/dx by implicit differentiation for the equation y cos(x) = 5x² - 3y², differentiate both sides of the equation with respect to x, using the chain rule on the left side and the product rule on the right side. Simplify the equation and solve for dy/dx in terms of x and y.
Step-by-step explanation:
To find dy/dx by implicit differentiation for the equation y cos(x) = 5x² - 3y², follow these steps:
- Differentiate both sides of the equation with respect to x.
- Use the chain rule on the left side and apply the product rule on the right side.
- Simplify the equation by collecting like terms.
- Finally, solve for dy/dx in terms of x and y.
The resulting derivative dy/dx will be the solution to the given problem.