product rule or chain rule how do you decide?

Hi please some one help me with the attached differentiation problem?

I get a bit confused in recognizing if it is a chain rule or product rule


I am aware if it is a chain rule then it has to be a function of a function


Thanks Zamzam

Product rule is when its a function times a function. Chain is when there is a function in a function that you can't do normally.

This would be a product rule, as e^(x/2) x sin(3x)

Is effectively that function, as you can see it is two functions multiplied by each other to form a product.

Surely it's chain rule to differentiate e^(x/2), chain rule to differentiate sin(3x) and then use those values in the product rule. Or am I missing something?

I think most of the time, those are seen as standard differentials. Like you can use chain rule but I think most people know what it is without the method?