What is (\partial)/(\partial x)(x^1y^2+y^4z^5) ?

The answer to (\partial)/(\partial x)(x^1y^2+y^4z^5) is y^2

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(\partial)/(\partial x)(x^1y^2+y^4z^5)

\frac{\partial}{\partial x} (x^{1} y^{2} + y^{4} z^{5})

y^{2}

Solution steps

\frac{\partial}{\partial x} (x^{1} y^{2} + y^{4} z^{5})

Simplify

x^{1} y^{2} + y^{4} z^{5} : x y^{2} + y^{4} z^{5}

= \frac{\partial}{\partial x} (x y^{2} + y^{4} z^{5})

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} (y^{4} z^{5})

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

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

= y^{2} + 0

Simplify

= y^{2}

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What is (\partial)/(\partial x)(x^1y^2+y^4z^5) ?
The answer to (\partial)/(\partial x)(x^1y^2+y^4z^5) is y^2