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

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

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

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

2 x + 9 z

Solution steps

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

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} (x^{2}) = 2 x

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

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

= 2 x + 0 + 9 z

Simplify

= 2 x + 9 z

t \to 0 - lim (t^{2} + 1)

\int e^{2 x} cos (e^{x}) d x

\frac{\partial}{\partial x} (cos^{3} (x^{4} y^{3}))

y^{^{''}} + 9 y = 27

x \to 2 + lim (x^{2} - 4)

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