Given 𝑢=𝑥2+𝑥𝑦+𝑦2, solve for ∂𝑢∂𝑥

To solve for ∂𝑢/∂𝑥, we need to take the partial derivative of 𝑢 with respect to 𝑥.

The given function is 𝑢=𝑥²+𝑥𝑦+𝑦².

The partial derivative of 𝑢 with respect to 𝑥 is obtained by differentiating each term of 𝑢 with respect to 𝑥, while treating all other variables as constants.

1. The derivative of 𝑥² with respect to 𝑥 is 2𝑥.
2. The derivative of 𝑥𝑦 with respect to 𝑥 is 𝑦 (since the derivative of 𝑥 is 1 and 𝑦 is treated as a constant).
3. The derivative of 𝑦² with respect to 𝑥 is 0 (since 𝑦² is a constant with respect to 𝑥).

So, ∂𝑢/∂𝑥 = 2𝑥 + 𝑦.