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

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

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

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

2 x - y

Solution steps

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

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

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

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

= 2 x - y + 0

Simplify

= 2 x - y

y^{2} = x^{2} - x c

\frac{d}{d x} (\frac{5 x}{1 + x ^{2}})

x \to 1 lim (\frac{x}{4 x - 1})

f (x) = x^{2}, (- 4, 15)

(8 x^{2} - 16 x + 16) e^{x}

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