What is (\partial)/(\partial x)(2xyz+xy^2+xz) ?

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

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(\partial)/(\partial x)(2xyz+xy^2+xz)

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

2 yz + y^{2} + z

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

= 2 yz + y^{2} + z

\frac{4 x}{x + 2}

x \to o lim (\frac{cos ( x )}{x})

\frac{d}{d x} (arccos (\frac{1 - x}{1 + x}))

x \cdot \frac{d y}{d x} - 2 \cdot y = 3 \cdot x^{2} + 2 \cdot x

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