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

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

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(\partial)/(\partial x)(x^2yz-xyz^3)

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

2 yz x - y z^{3}

Solution steps

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

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^{3})

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

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

= 2 yz x - y z^{3}

y = 7 x, y = x^{2} - 8

f (x) = \frac{x}{x + 9}

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

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

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

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