E(y)= y*ln(1+e^y^2) find the first derivative

is this correct dE/dy *ln(1+e^y^2)+y*(1/1+e^y^2)*e^y^2(2y*dE/dy) ? thank you

Not quite -- you kind of got carried away.

Why do you have dE/dy n the right?
You should have said

dE/dy = ln(1+e^y^2) + y * 1/(1+e^y^2) * e^y^2 *(2y)