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,


`(\mathrm d(f\circ c))/(\mathrm dt)=\\abla f(c(t))\cdot(\mathrm dc)/(\mathrm dt)`

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


`\\abla f(c(\pi))\cdot c'(\pi)=\\abla 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`