this is a little confusing
f(x) = e^xsinx
i don't know what rule to use with this
Then use the chain rule.
$\displaystyle \frac{d}{dx} e^u = e^u \frac{du}{dx}$
Hence:
$\displaystyle f'(x) = e^{x \sin x} \left(\frac{d}{dx} x \sin x \right)$
Applying the product rule to the leftover derivative:
$\displaystyle f'(x) = e^{x \sin x} (x \cos x + \sin x)$
The product rule does not change based on situations. In your example, u was a function of x, which prompted us to use the chain rule to evaluate the derivative. The fact that du/dx required us to use the product rule was a function (pardon the pun) of the function $\displaystyle u(x) = x \sin x$.