Question

Let v(s) = . Evaluate d/ds v[g(s)] at s = 4 given that g(4) = 3 and g'(4) = -9 d/ds v[g(s)] = v'[g(s)]g'(s). Please help

Answer 1

\(\dfrac{d}{ds}v(g(s))\), right?

Answer 2

\(v(s) =<s^2, 2s, 9/s^2>\\v(g(s)) = <g^2(s), 2g(s), 9/(g^2(s))>\)

now, just take derivative of it w.r.t s
\(\dfrac{d}{ds}(v(g(s)) = <2g(s). g'(s), 2g(s)', I~let~you~do~the~last~one>\)

Now, replace s =4 to get the answer
it should be <2*3*(-9), 2*(-9) , your work>

Answer 3

Thank you