What is (\partial)/(\partial x)(xy^2-2y^3+3xz) ?

The answer to (\partial)/(\partial x)(xy^2-2y^3+3xz) is y^2+3z

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(\partial)/(\partial x)(xy^2-2y^3+3xz)

\frac{\partial}{\partial x} (x y^{2} - 2 y^{3} + 3 x z)

y^{2} + 3 z

Solution steps

\frac{\partial}{\partial x} (x y^{2} - 2 y^{3} + 3 x z)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y^{2}) - \frac{\partial}{\partial x} (2 y^{3}) + \frac{\partial}{\partial x} (3 x z)

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

\frac{\partial}{\partial x} (2 y^{3}) = 0

\frac{\partial}{\partial x} (3 x z) = 3 z

= y^{2} - 0 + 3 z

Simplify

= y^{2} + 3 z

n = 0 \sum \infty \frac{n !}{n ^{3}}

\frac{d}{d x} ((2 x + 3)^{\frac{1}{2}})

\frac{\partial}{\partial x} (3 x^{2} y)

\frac{d}{d x} (sin (x - 2))

\frac{d}{d x} (\frac{( 4 x - 4 ) ^{5}}{( 2 x - 5 ) ^{7}})

What is (\partial)/(\partial x)(xy^2-2y^3+3xz) ?
The answer to (\partial)/(\partial x)(xy^2-2y^3+3xz) is y^2+3z