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

The answer to (\partial)/(\partial z)(x^2yz+1/(xyz^2)) is x^2y-2/(xyz^3)

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

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

x^{2} y - \frac{2}{x y z ^{3}}

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial z} (\frac{1}{x y z ^{2}}) = - \frac{2}{x y z ^{3}}

= x^{2} y - \frac{2}{x y z ^{3}}

\int \frac{1}{25 x ^{2} + 2} d x

2 x y y^{^{'}} = 3 y^{2} + x^{2}

\int \frac{e ^{x}}{( e ^{x} - 4 ) ( e ^{2 x} + 1 )} d x

\frac{d}{d x} (sin (3 x) cos (2 x))

What is (\partial)/(\partial z)(x^2yz+1/(xyz^2)) ?
The answer to (\partial)/(\partial z)(x^2yz+1/(xyz^2)) is x^2y-2/(xyz^3)