What is (\partial)/(\partial x)(x^2yz-xyz^5) ?

The answer to (\partial)/(\partial x)(x^2yz-xyz^5) is 2yzx-yz^5

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(\partial)/(\partial x)(x^2yz-xyz^5)

\frac{\partial}{\partial x} (x^{2} yz - x y z^{5})

2 yz x - y z^{5}

Solution steps

\frac{\partial}{\partial x} (x^{2} yz - x y z^{5})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2} yz) - \frac{\partial}{\partial x} (x y z^{5})

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

\frac{\partial}{\partial x} (x y z^{5}) = y z^{5}

= 2 yz x - y z^{5}

y^{^{'''}} - y^{^{''}} + 7 y^{^{'}} - 7 y = 0

x \to 0 lim (x^{3} x)

\int_{0}^{5} \frac{x + y}{55} d x

\frac{\partial}{\partial x} (4 arctan (\frac{y}{x}))

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

What is (\partial)/(\partial x)(x^2yz-xyz^5) ?
The answer to (\partial)/(\partial x)(x^2yz-xyz^5) is 2yzx-yz^5