What is (\partial)/(\partial x)(3xy^2z^3-xyz) ?

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

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(\partial)/(\partial x)(3xy^2z^3-xyz)

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

3 y^{2} z^{3} - yz

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 3 y^{2} z^{3} - yz

x \to - 1 lim (x^{2} - 4 x)

\frac{\partial}{\partial x} (x cos (π y))

x \to - \infty lim (e^{- x})

e^{2^{x^{2} + 3 x + 1}}

\int 22 cos (0.25 x) sin (0.5 x) d x

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