An air pollution index is $p=x^2+2xy+4xy^2$. At the point $(10,5)$, the partial derivatives $\dfrac{\partial p}{\partial x}$ and $\dfrac{\partial p}{\partial y}$ are:

1. Differentiate with respect to $x$, treating $y$ as constant: $\dfrac{\partial p}{\partial x}=2x+2y+4y^2$. 2. At $(10,5)$: $20+10+4(25)=20+10+100=130$. 3. Differentiate with respect to $y$, treating $x$ as constant: $\dfrac{\partial p}{\partial y}=2x+8xy$. 4. At $(10,5)$: $20+8(10)(5)=20+400=420$. 5. Substituting the point before differentiating, a common slip, leaves an $x$ or $y$ still in the answer. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 10: Differentiation_