What is (\partial}{\partial z}(\frac{x^2+z^2)/y+xyz+5xz^2) ?

The answer to (\partial}{\partial z}(\frac{x^2+z^2)/y+xyz+5xz^2) is (2z)/y+xy+10xz

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(\partial}{\partial z}(\frac{x^2+z^2)/y+xyz+5xz^2)

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

\frac{2 z}{y} + x y + 10 x z

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial z} (5 x z^{2}) = 10 x z

= \frac{2 z}{y} + x y + 10 x z

\int \frac{e ^{x} + 1}{e ^{x} - 1} d x

\frac{\partial}{\partial x} (a sin (x) sin (y))

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

\frac{\partial}{\partial x} (\frac{2 s - 3 t}{3 s + 5 t})

What is (\partial}{\partial z}(\frac{x^2+z^2)/y+xyz+5xz^2) ?
The answer to (\partial}{\partial z}(\frac{x^2+z^2)/y+xyz+5xz^2) is (2z)/y+xy+10xz