Question

How do you differentiate the following parametric equation: `x(t)=t^2cos^2t, y(t)=tsint`?

Answer 1

`dy/dx = ( sint + t cos t ) / ( 2t cos^2 t - 2t^2 cos t sin t )`

Explanation:

`x(t)=t^2cos^2t, y(t)=tsint`

`dx/dt =2tcos^2t + t^2 (2) cos t (-sin t) = 2t cos^2 t - 2t^2 cos t sin t`

`dy/dt =sint + t cos t`

`dy/dx = (dy/dt)/(dx/dt) = ( sint + t cos t ) / ( 2t cos^2 t - 2t^2 cos t sin t )`