What is (\partial)/(\partial x)(x^2-xy+3y^2) ?

The answer to (\partial)/(\partial x)(x^2-xy+3y^2) is 2x-y

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(\partial)/(\partial x)(x^2-xy+3y^2)

\frac{\partial}{\partial x} (x^{2} - x y + 3 y^{2})

2 x - y

Solution steps

\frac{\partial}{\partial x} (x^{2} - x y + 3 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (3 y^{2})

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (x y) = y

\frac{\partial}{\partial x} (3 y^{2}) = 0

= 2 x - y + 0

Simplify

= 2 x - y

\frac{\partial}{\partial x} (2 x y + x^{2} - 1)

x \to 3 lim (- 3 x - 6)

\frac{d}{d x} (x (1 - cos (x)))

\int_{0}^{2} (4 x^{3} - 3 x^{2} + 2 x) d x

\int \frac{1}{5} e^{\frac{- y}{5}} d y

What is (\partial)/(\partial x)(x^2-xy+3y^2) ?
The answer to (\partial)/(\partial x)(x^2-xy+3y^2) is 2x-y