What is (\partial)/(\partial x)(1+xy^2-2z^2) ?

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

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(\partial)/(\partial x)(1+xy^2-2z^2)

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

y^{2}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (1) = 0

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

\frac{\partial}{\partial x} (2 z^{2}) = 0

= 0 + y^{2} - 0

Simplify

= y^{2}

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\frac{d}{d x} (\frac{1}{( - 3 x ^{2} + 3 x - 2 ) ^{3}})

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