Asked by Zoe
fin derivative of the function
(t+e^t)(4- sqrt t)
(t+e^t)(4- sqrt t)
Answers
Answered by
drwls
Use the product rule
d/dt (u*v) = u*dv/dt + v*du/dt
and you get
(t + e^t)[-1/(2*sqrt t)]
+ (1 + e^t)(4 - sqrt t)
Or you could multiply out u(t)*v(t) and differentiate it term by term
u*v = 4t + 4e^t -t^3/2 -e^t*t^1/2
d/dt(u*v) = 4 + 4e^t -(3/2)t^1/2 -e^t*t^1/2 -(1/2)e^t/t^1/2
d/dt (u*v) = u*dv/dt + v*du/dt
and you get
(t + e^t)[-1/(2*sqrt t)]
+ (1 + e^t)(4 - sqrt t)
Or you could multiply out u(t)*v(t) and differentiate it term by term
u*v = 4t + 4e^t -t^3/2 -e^t*t^1/2
d/dt(u*v) = 4 + 4e^t -(3/2)t^1/2 -e^t*t^1/2 -(1/2)e^t/t^1/2