What is (\partial)/(\partial y)(y^{xz}+2(yz)^x) ?

The answer to (\partial)/(\partial y)(y^{xz}+2(yz)^x) is xzy^{xz-1}+2xz^xy^{x-1}

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(\partial)/(\partial y)(y^{xz}+2(yz)^x)

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

x z y^{x z - 1} + 2 x z^{x} y^{x - 1}

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (y^{x z}) = x z y^{x z - 1}

\frac{\partial}{\partial y} (2 (yz)^{x}) = 2 x z^{x} y^{x - 1}

= x z y^{x z - 1} + 2 x z^{x} y^{x - 1}

What is (\partial)/(\partial y)(y^{xz}+2(yz)^x) ?
The answer to (\partial)/(\partial y)(y^{xz}+2(yz)^x) is xzy^{xz-1}+2xz^xy^{x-1}