What is (\partial)/(\partial x)(x^2+2y^2+9xz-12) ?

The answer to (\partial)/(\partial x)(x^2+2y^2+9xz-12) is 2x+9z

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(\partial)/(\partial x)(x^2+2y^2+9xz-12)

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 9 x z - 12)

2 x + 9 z

Solution steps

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 9 x z - 12)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (2 y^{2}) + \frac{\partial}{\partial x} (9 x z) - \frac{\partial}{\partial x} (12)

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

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

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

\frac{\partial}{\partial x} (12) = 0

= 2 x + 0 + 9 z - 0

Simplify

= 2 x + 9 z

What is (\partial)/(\partial x)(x^2+2y^2+9xz-12) ?
The answer to (\partial)/(\partial x)(x^2+2y^2+9xz-12) is 2x+9z