Question

What is the derivative of `f(t) = (t-lnt^2, t^2-sint )`?

Answer 1

`dy/dx=(2t^2-tcost)/(t-2)`

Explanation:

Given `x=f(t),y=g(t)`

`dy/dx=(dy/dt)/(dx/dt)`

`dy/dt=g'(t)=2t-cost`

`dx/dt=f'(t)=1-(2t)/t^2=1-2/t`

`dy/dx=(2t-cost)/(1-2/t)=(2t-cost)/((t-2)/t)=(2t^2-tcost)/(t-2)`