What is (\partial)/(\partial y)(x^2yz+1/(xyz^2)) ?

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

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(\partial)/(\partial y)(x^2yz+1/(xyz^2))

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

x^{2} z - \frac{1}{x z ^{2} y ^{2}}

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= x^{2} z - \frac{1}{x z ^{2} y ^{2}}

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