Give a function f(x)= ln(3x^(e^x)+2). Find the derivative f'(x) of the function.

Solution:

As we use the chain rule and the power rule, we can get ln(3x^(e^x)+2) =  1/(3x^(e^x)+2) * e^x* 3x^(e^x-1)*e^x. When we simplify it, we can get f'(x) = (e^(2x))(3x^(e^x-1)/(3x^(e^x)+2).