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

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

(\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

d er i v a t i v e (2 x - 8)^{4} (x^{2} + x + 1)^{5}

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

\int e^{- x^{2}} \cdot (- 2 x^{3}) d x

\int_{0}^{1} 2 - x^{2} d x

x \to 0 lim (\frac{1 + cos ( x )}{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