Let , where and are differentiable scalar functions and is differentiable. Which of…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let r(t)=⟨f(g(t)), h(t)⟩r(t)=\langle f(g(t)),\,h(t)\rangle, where ff and gg are differentiable scalar functions and hh is differentiable. Which of the following expressions gives drdt\dfrac{dr}{dt} in terms of f, gf,\,g, and hh? (a) ⟨f′(t) g′(t), h′(t)⟩\left\langle f'(t)\,g'(t),\,h'(t)\right\rangle (b) ⟨f′(g(t)), h′(t)⟩\left\langle f'(g(t)),\,h'(t)\right\rangle (c) ⟨f(g(t)) g′(t), h′(t)⟩\left\langle f(g(t))\,g'(t),\,h'(t)\right\rangle (d) ⟨f′(g(t)) g′(t), h′(t)⟩\left\langle f'(g(t))\,g'(t),\,h'(t)\right\rangle

Related theory

Browse the problem library