Let for . Define the scalar function and the vector function . The combined position…

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

Problem

Let

u=g(t)=\sqrt{t}

for

t>0

. Define the scalar function

s(u)=u^{2}

and the vector function

\mathbf r(u)=\langle e^{u},\,\tan u\rangle

. The combined position vector is

\mathbf p(t)=s(u)\,\mathbf r(u)

. Find

\dfrac{d\mathbf p}{dt}

in terms of

t