Question

How do you differentiate the following parametric equation: `x(t)=te^t , y(t)=e^t/t`?

Answer 1

`dy/dx=1/t^2((t-1)/(t+1)), t ne0,-1`

Explanation:

`y(t)=e^t/t`

Diff.ing w.r.t. `t`, using the Quotient Rule, we have,

`dy/dt={td/dt(e^t)-e^td/dt(t)}/t^2=(te^t-e^t)/t^2=(e^t(t-1))/t^2`.

Similarly, we have, `dx/dt=te^t+e^t=e^t(t+1)`.

Finally, by the Rule of Parametric Diffn., we have,

`dy/dx=(dy/dt)/(dx/dt)=1/t^2((t-1)/(t+1)), t ne0,-1`