In one or two sentences

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

Problem

In one or two sentences, explain why differentiating

\mathbf r(t)=\langle f(g(t)),\,h(g(t)),\,k(g(t))\rangle

component by component produces the correct overall derivative

\dfrac{d\mathbf r}{dt}