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

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

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

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

2 z^{2}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 2 z^{2}

Simplify

= 2 z^{2}

\frac{d}{d x} (\frac{2}{4 x + 1})

\frac{d}{d x} (arctan (\frac{x}{3}))

\frac{d}{d x} (3 2 x - x^{2})

\frac{e ^{- s}}{s ^{2} - s + 1}

\frac{d y}{d t} + 20 y = 60, y (0) = 0

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