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

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

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

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

2 x + 3 y

Solution steps

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

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

\frac{\partial}{\partial x} (3 x y) = 3 y

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

= 2 x + 3 y - 0

Simplify

= 2 x + 3 y

x \frac{d y}{d x} + 3 y = \frac{e ^{x}}{x ^{2}}

\int x (x + 4)^{\frac{1}{3}} d x

(2 x - 8)^{4} (x^{2} + x + 1)^{5}

\frac{3}{5 s}

\frac{d}{d x} (9 sin (x) - sin (9 x))

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