Final answer:
To find dy/dx by implicit differentiation for the equation y cos x = 4x² - 5y², differentiate both sides of the equation with respect to x. Rearrange the equation and solve for dy/dx to get dy/dx = (8x - y sin x)/(10y + cos x).
Step-by-step explanation:
To find dy/dx by implicit differentiation for the equation y cos x = 4x² - 5y², we need to differentiate both sides of the equation with respect to x.
Differentiating y cos x, we get (dy/dx) cos x - y sin x. Differentiating 4x² - 5y², we get 8x - 10y(dy/dx). Setting these two expressions equal to each other, we have (dy/dx) cos x - y sin x = 8x - 10y(dy/dx). Rearranging the equation and solving for dy/dx, we get dy/dx = (8x - y sin x)/(10y + cos x).