1. The problem statement, all variables and given/known data f(x)= x^(3)e^(x) Find f'(x) in simplest form. Find f"(x) in simplest form. 2. Relevant equations 3. The attempt at a solution I found the first derivative to be: (using the product rule) f'(x) = (e^x)[3x^2] + (x^3)[e^x] f'(x) = 3x^(2)e^(x) + x^(3)e^(x) f'(x) = x^e^[x](3 + x) I'm really not sure how to find f"(x) because of the "e". My initial thoughts would be to use the def. of derivatives on the problem, but then I get confused as to whether I should use the unfactored f'(x) or the factored version, which as far as I can tell would require the product rule. If anyone could help me get to f"(x) that would be great. Thank you! Also, the next part says to find the slope of the line tangent to the graph of f(x) at two different x values. Would I use f'(x) or f"(x) for this?