What is (\partial)/(\partial x)(x^2y+2y^2-6x+3y-4) ?

The answer to (\partial)/(\partial x)(x^2y+2y^2-6x+3y-4) is 2xy-6

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(\partial)/(\partial x)(x^2y+2y^2-6x+3y-4)

\frac{\partial}{\partial x} (x^{2} y + 2 y^{2} - 6 x + 3 y - 4)

2 x y - 6

Solution steps

\frac{\partial}{\partial x} (x^{2} y + 2 y^{2} - 6 x + 3 y - 4)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (2 y^{2}) - \frac{\partial}{\partial x} (6 x) + \frac{\partial}{\partial x} (3 y) - \frac{\partial}{\partial x} (4)

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

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

\frac{\partial}{\partial x} (6 x) = 6

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

\frac{\partial}{\partial x} (4) = 0

= 2 y x + 0 - 6 + 0 - 0

Simplify

= 2 x y - 6

\int \frac{2}{1 - x ^{2}} d x

\frac{d}{d y} (e^{y z})

f (x) = x^{3} (3 x - 5)^{2}

\int_{1}^{2} \frac{6}{x ^{2}} d x

\int_{- 3}^{3} (2 - ∣ x ∣) d x

What is (\partial)/(\partial x)(x^2y+2y^2-6x+3y-4) ?
The answer to (\partial)/(\partial x)(x^2y+2y^2-6x+3y-4) is 2xy-6