Given y = 2sin(θ) and x = 3cos(θ) find dy/dx.

The function is defined parametrically so we usually approach these questions using chain rule.Recall that: dy/dθ * dθ/dx = dy/dx So we will need to differentiate each expression individually then multiply them together.Differentiating the first with respect to θ we get:(1)   dy/dθ = 2cos(θ) ,then the expression for x gives us: dx/dθ = -3sin(θ) , We can then remember that differentials behave as fractions so we can flip both sides to get:(2)  dθ/dx = -1/3sin(θ) . Remembering chain rule we can multiply (1)*(2) to get dy/dx: dy/dθ * dθ/dx = 2cos(θ) * -1/3sin(θ) --> dy/dx = -2cos(θ)/3sin(θ)