Question

Help
Use the Product Rule to calculate:
dy/dt t=2, y=(t-8t^-1)(e^t+t^2)

Answer 1

when F(t) can be written as f(t)g(t):\[F'(t) = f'(t)g(t) + g'(t)f(t)\]
in this case, f(t) = (t - 8t^(-1)) and g(t) = (e^t + t^2)

Answer 2

do you mean this??
f(t)= (t-8t^-1). (e^t+t^2)' + (e^t+t^2).(t-8t^-1)'

Answer 3

yes

Answer 4

ok. I multiplied them and i got
(et^2+2t^2-8e-16)+(8t+8)
am i right ?

Answer 5

idk how you simplified it.

use wolfram or something

Answer 6

I'm not sure of my answer. I foiled/ muliplied everything and that's what i got

Answer 7

dy/dt t=2, y=(t-8t^-1)(e^t+t^2)

f'(x)= [1+8t^(-2)][e^(t)+t^2]+[e^(t)+2t][t-8t^(-1)]