Find the derivative of the vector function r(t)=ta×(b+tc)r(t)=ta×(b+tc), where a=⟨5,3,−4⟩a=⟨5,3,−4⟩, b=⟨−4,1,1⟩b=⟨−4,1,1⟩, and c=⟨−3,2,−4⟩c=⟨−3,2,−4⟩.