Final answer:
To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. Apply the product rule and isolate dy/dx by moving terms.
Step-by-step explanation:
To find dy/dx by implicit differentiation, we'll differentiate both sides of the equation with respect to x. Let's start by differentiating y cos x = 5x2 + 3y2:
Using the product rule, we have: dy/dx * cos x + y * (-sin x) = 10x + 6y * dy/dx
Next, isolate dy/dx by moving terms:
dy/dx * cos x - 6y * dy/dx = 10x - y * (-sin x)
dy/dx * (cos x - 6y) = 10x + y * sin x
dy/dx = (10x + y * sin x) / (cos x - 6y)