Hello!!

Question

1. find the third derivative of

f(t)=(t-1)/(t+1)

2.

y= x^(x^2) ; dy/dx

please help! thank you!

Answer 1

f = (t-1)/(t+1)
f' = 2/(t+1)^2
now it's easy
f'' = -4/(t+1)^3
f''' = 12/(t+1)^4

y = x^(x^2)
lny = x^2 ln x
1/y y' = 2x lnx + x^2/x
y' = y(2x ln x + x)
and plug back in y = x^(x^2)