Find the derivative of:

g(x)=ln(ln(x+1))+e^(x^(3/2)+(x/3))

Use the chain rule separately on each of the two terms

[1/(ln(x+1)]*[1/(x+1)] +
e^(x^(3/2)+(x/3))* [(3/2)x^1/2 + (1/3)]