Question

Ts marsvectorcalc6 2.5.033. ask your teacher my notes question part points submissions used let f: double-struck r4 → double-struck r and c(t): double-struck r → double-struck r4. suppose ∇f(1, 1, π, e6) = (0, 1, 3, −9), c(π) = (1, 1, π, e6), and c'(π) = (18, 13, 0, 1). find d(f ∘
c.dt when t = π.

Answer 1

By the chain rule,

$\dfrac{\mathrm d(f\circ c)}{\mathrm dt}=\nabla f(c(t))\cdot\dfrac{\mathrm dc}{\mathrm dt}$

When $t=\pi$, the derivative has a value of

$\nabla f(c(\pi))\cdot c'(\pi)=\nabla f(1,1,\pi,e^6)\cdot(18,13,0,1)=(0,1,3,-9)\cdot(18,13,0,1)=0+13+0-9=4$