How do you differentiate the following parametric equation: $x(t)=(t+1)e^t, y(t)= t-e^(t-1)$ ?

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Answer 1 · 2017-07-02T06:53:10

$(dy)/(dx)=(1-e^(t-1))/((t+2)e^t)$

In parametric form of equations, $(dy)/(dx)=((dy)/(dt))/((dx)/(dt))$

Here $x(t)=(t+1)e^t$ and therefore

$(dx)/(dt)=e^t+(t+1)e^t=(t+2)e^t$

and as $y(t)=t=e^(t-1)$ , $(dy)/(dt)=1-e^(t-1)$

Hence $(dy)/(dx)=(1-e^(t-1))/((t+2)e^t)$

How do you differentiate the following parametric equation: x(t)=(t+1)e^t, y(t)= t-e^(t-1) x(t)=(t+1)e^t, y(t)= t-e^(t-1) ?