Question

y = 3t² + sint
x = 2sint + cost.

Now find dx/dy .

Answer 1

Hey there !

We observe that both x, y are in terms of t.

Differentiating y with respect to t

dy/dt = d ( 3t²+sint)/dt = 3(2)t +cost

Differentiating x with respect to t.

dx/dt = d ( 2sint + cost ) / dt = 2(cost)-sint.

Now, dx/dy = dx/dt / dy/dt = 2cost - sint / 6t + cost.

Hope helped!

Answer 2

Given x = 3t^2 + sint

dx/dt = d/dt(2sint + cost)

          = d/dt(2sint) + d/dt(2cost)

          = 2cost - sint.



dy/dt = d/dt(3t^2 + sint)

          = d/dt(3t^2) + d/dt(sint)

           = 6t + cost.



Therefore:

dx/dy = dx/dt /   dy/dt

           = 2cost - sint/6t + cost


Hope this helps!