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

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

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

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

2 x + 2 y

Solution steps

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

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

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

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

= 2 x + 2 y + 0

Simplify

= 2 x + 2 y

\int \frac{1}{u} d u

y^{^{''}} - 2 y^{^{'}} - 15 y = 0

(4 y + y x^{2}) d y = (2 x + x y^{2}) d x

\frac{d}{d x} (8 e^{2 x} x + 12 e^{2 x})

6 - x^{2}, 8 - 3 x

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