Question

Differentiate each function;

Answer 1

This function is first and foremost a PRODUCT. We could also write it as x/e^(x^2), a QUOTIENT. Try applying the quotient rule to the latter expression. Let me know whether or not this makes sense.

Answer 2

@mathmale
I see that a product rule is applied first then a chain rule but I am not sure how to start.

Answer 3

Please review the product rule.
I'll summarize it here: (uv)' = uv' + vu'
In the function you present, u = x and v = e^(x^2).
u' = 1 and v' = e^(x^2) * (x^2)' (which is an application of the chain rule).
Can you take the problem solution from here?

Answer 4

@mathmale
so is the setup like this;
x(d/dx(e^(x)^(2))+e^(x)^(2)(d/dx(x))

Answer 5

Your handwritten expression is the better one, as you've used hand-drawn parentheses perfectly there. Now please find the two derivatives (each one inside a BIG set of parentheses) and simplify the result. Just one oversight: that's e^(-x^2) [not e^(x^2), if you're using the product rule. Otherwise you're right on target!!