Question

If x = a(Cos(t) + t^2) and y = a(Sin(t) + t^2 + t^3) then dy/dx equals to

(a) (Cos(t) + 3t^2 + 2t) / (-Sin(t) + 2t)

(b) (Sin(t) + 3t^2 + 2t) / (-Cos(t) + 2t)

(c) (Sin(t) + 3t^2 + 2t) / (Cos(t) + 2t)

(d) (Cos(t) + 3t^2 + 2t) / (Sin(t) + 2t)

I have been asked this question in class test.

My query is from The nth Derivative of Some Elementary Functions in portion Differential Calculus of Engineering Mathematics

Answer 1

The correct choice is (a) (Cos(t) + 3t^2 + 2t) / (-Sin(t) + 2t)

To explain I would say: dx/dt = a(-Sin(t) + 2t)

dy/dt = a(Cos(t) + 2t + 3t^2)

Then,

dy/dx = (Cos(t) + 3t^2+2t)/(-Sin(t) + 2t).