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

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

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

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

2 x y + y + 3

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

= 3 + y + 2 y x - 0

Simplify

= 2 x y + y + 3

\frac{\partial}{\partial x} (\frac{1}{∣ x ∣})

\int_{0}^{2} 2 x + 5 d x

\frac{d}{d x} (40 x (5 x^{2} - 8))

\int_{2}^{\infty} \frac{1}{x ^{5}} d x

\int x e^{\frac{x ^{2}}{2}} d x

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