Mathematics

Problem

The path of a particle is described by

x=te^{t},\qquad y=e^{t},\qquad t\in\mathbb R.

(i) Obtain

\dfrac{dy}{dx}

in terms of

t

. (ii) Determine the value(s) of

t

for which the tangent to the curve is (a) horizontal and (b) vertical. (iii) Eliminate

t

to express

\dfrac{dy}{dx}

solely in terms of

x

and

y