What is (\partial)/(\partial x)(4z^5+x^4y-y^5x) ?

The answer to (\partial)/(\partial x)(4z^5+x^4y-y^5x) is -y^5+4x^3y

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(\partial)/(\partial x)(4z^5+x^4y-y^5x)

\frac{\partial}{\partial x} (4 z^{5} + x^{4} y - y^{5} x)

- y^{5} + 4 x^{3} y

Solution steps

\frac{\partial}{\partial x} (4 z^{5} + x^{4} y - y^{5} x)

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 z^{5}) + \frac{\partial}{\partial x} (x^{4} y) - \frac{\partial}{\partial x} (y^{5} x)

\frac{\partial}{\partial x} (4 z^{5}) = 0

\frac{\partial}{\partial x} (x^{4} y) = 4 y x^{3}

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

= 0 + 4 y x^{3} - y^{5}

Simplify

= - y^{5} + 4 x^{3} y

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What is (\partial)/(\partial x)(4z^5+x^4y-y^5x) ?
The answer to (\partial)/(\partial x)(4z^5+x^4y-y^5x) is -y^5+4x^3y