Question

calculate Z(t) and dz/dt for : I'll post in a second

Answer 1

\[f(x,y)= x^2 e^y\]

\[x(t)=t^2-1\]

\[y(t)=\sin(t)\]

Answer 2

first dz/dt = fx dx/dt + y dy/dt which will be:

\[dz/dt = 4t^2 (t^2-1)e^sint + (t^2-1)^2 \cos(t) e^sint\]

Answer 3

^ in this case e is to the power sint , not sure why it didn't work.

Answer 4

the problem now is z(t) , my answer: " please correct ":

\[z(t)=(2t,cost)\]

Answer 5

wait since dz/dt = \[2xe^y*2t + x^2e^y *cost\]

shouldn't z(t)= \[4t^2 (t^2-1) e^sint + (t^2-1)^2 cost * e^sint\]

e is to the power of sint

Answer 6

as far as I am aware u just figured it out

Answer 7

so since my first answer really is a lead to my second answer which is the correct one , if we wanted to evaluate ?

Answer 8

keep going

Answer 9

I think that's what I know :D , I think the next thing I should do is just simplifying.