Question

derivative of t^(t^2/2) ?

Answer 1

?
\[\huge \frac{d}{dt}t^{\frac{t^2}2}\]
this?

Answer 2

yes

Answer 3

Well, start with this...
\[\huge y =t^{\frac{t^2}2} \]

Answer 4

And get the natural logarithm of both sides ^.^ Logs are great, they turn exponents into products... sort of...
\[\huge \ln \ y =\ln \ t^{\frac{t^2}2} \]

Answer 5

And there's this one neat property of logarithms that allows you to do this...
\[\huge \ln \ y = \frac{t^2}{2} \ \ln t\]
Now feel free to differentiate implicitly... and you can thank me later :P