My textbook had $$\frac{d}{dx}\left(x+y+e^{xy}\right)=1+\frac{dy}{dx}+e^{xy}\left(y+x\frac{dy}{dx}\right)$$ as part of an example problem.
Why does $\frac{d}{dx}(e^{xy})$ equal $e^{xy}(y+x\frac{dy}{dx})$?
Why does it not simply equal $ye^{xy}$ ?
Is there something about the chain rule I am missing?
The product rule: $$\frac{d}{dx}(uv)=u\frac{dv}{dx}+v\frac{du}{dx}$$
So we need to find $\frac{d}{dx}(e^{xy})$.
We know that $$\frac{d}{dx}(e^{xy})=\frac{d}{dx}(xy)\cdot e^{xy}$$
Letting $u=x$ and $v=y$, can you proceed from here?