Question

How do you differentiate the following parametric equation: `x(t)=te^t+5t, y(t)= t^2-3e^(t)`?

Answer 1

`dy/dx=((t+1)e^t+5)/(2t-3e^t).`

Explanation:

By Defn., `dy/dx=(dy/dt)/(dx/dt)`

`y=y(t)=t^2-3e^t rArr dy/dt=d/dt(t^2-3e^t)=d/dt(t^2)-d/dt(3e^t)`

`=2t-3e^t`

`x=x(t)=te^t+5t rArr dx/dt=d/dt(te^t+5t)=d/dt(te^t)+d/dt(5t)`

`=td/dt(e^t)+e^td/dt(t)+5=te^t+e^t+5=(t+1)e^t+5`

`:. dy/dx=((t+1)e^t+5)/(2t-3e^t).`