What is (\partial)/(\partial x)(x^2y+2xz+2y^2+6z+9) ?

The answer to (\partial)/(\partial x)(x^2y+2xz+2y^2+6z+9) is 2xy+2z

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(\partial)/(\partial x)(x^2y+2xz+2y^2+6z+9)

\frac{\partial}{\partial x} (x^{2} y + 2 x z + 2 y^{2} + 6 z + 9)

2 x y + 2 z

Solution steps

\frac{\partial}{\partial x} (x^{2} y + 2 x z + 2 y^{2} + 6 z + 9)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (2 x z) + \frac{\partial}{\partial x} (2 y^{2}) + \frac{\partial}{\partial x} (6 z) + \frac{\partial}{\partial x} (9)

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

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

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

\frac{\partial}{\partial x} (6 z) = 0

\frac{\partial}{\partial x} (9) = 0

= 2 y x + 2 z + 0 + 0 + 0

Simplify

= 2 x y + 2 z

\frac{\partial}{\partial t} (x z t^{2} y + 1)

\int e^{x} 1 + e^{x} d x

\frac{A}{y ^{10}} + B e^{y}

y = x + 1, y = x^{2} - 1

\int \frac{x ^{2} - x + 30}{x ^{3} + 5 x} d x

What is (\partial)/(\partial x)(x^2y+2xz+2y^2+6z+9) ?
The answer to (\partial)/(\partial x)(x^2y+2xz+2y^2+6z+9) is 2xy+2z