The motion of a point on a curve is described parametrically for by x=e^ 3t

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The motion of a point on a curve is described parametrically for

t>0

x=e^{3t},\qquad y=t^{2}\,\ln(e^{t}).

(i) Obtain

\dfrac{dy}{dx}

in terms of

t

. (ii) Hence find

\dfrac{d^{2}y}{dx^{2}}

in terms of

t