Question

Calculuate d/dt f(c(t)) when f(x,y) = 3x - 7y and c(t) = (cost, sint) and t=0

Answer 1

$$(f\circ c)(t)=3\cos t-7\sin t\\\frac{d}{dt}(3\cos t-7\sin t)=-3\sin t-7\cos t\\-3\sin(0)-7\cos(0)=-7$$