I have this velocity field, of which I have to get the material derivative: $$\mathbf u(x,y)=\sin(x-y)\mathbf i-\cos(x-y)\mathbf j$$ Where i & j are the vector field components. Seems pretty straightforward: $$\mathbf a=\mathbf u \cdot \nabla \mathbf u$$
$$\mathbf a=(\cos(x-y)-\sin(x-y))(\sin(x-y)\mathbf i-\cos(x-y)\mathbf j$$ But apparently the correct answer is: $$\mathbf a=(\sin(x-y)+\cos(x-y))(\cos(x-y)\mathbf i+\sin(x-y)\mathbf j$$ Did I not simplify right? Or am I missing something?
$$ \boldsymbol u \cdot \nabla \boldsymbol u = (u_1 \partial_x + u_2\partial_y)\boldsymbol{u} $$
I think you have the order wrong.