Mathematics

Problem

Let

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

, where

f

and

g

are differentiable scalar functions and

h

is differentiable. Which of the following expressions gives

\dfrac{dr}{dt}

in terms of

f,\,g

, and

h

? a)

\left\langle f'(t)\,g'(t),\,h'(t)\right\rangle

\left\langle f'(g(t)),\,h'(t)\right\rangle

\left\langle f(g(t))\,g'(t),\,h'(t)\right\rangle

\left\langle f'(g(t))\,g'(t),\,h'(t)\right\rangle