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

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

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

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

2 x y + z^{2}

Solution steps

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

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

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

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

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

= 2 y x + 0 + z^{2}

Simplify

= 2 x y + z^{2}

\frac{d}{d x} (\frac{3 x + 2}{5 - 4 x})

\int x^{7} d x

\int \frac{2}{12 - 5 x} d x

arccos (x)

(1 + x)^{- \frac{4}{3}}

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