What is (\partial)/(\partial y)(xyz+xy^3+yz^3+zx^3) ?

The answer to (\partial)/(\partial y)(xyz+xy^3+yz^3+zx^3) is xz+3xy^2+z^3

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(\partial)/(\partial y)(xyz+xy^3+yz^3+zx^3)

\frac{\partial}{\partial y} (x yz + x y^{3} + y z^{3} + z x^{3})

x z + 3 x y^{2} + z^{3}

Solution steps

\frac{\partial}{\partial y} (x yz + x y^{3} + y z^{3} + z x^{3})

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x yz) + \frac{\partial}{\partial y} (x y^{3}) + \frac{\partial}{\partial y} (y z^{3}) + \frac{\partial}{\partial y} (z x^{3})

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

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

\frac{\partial}{\partial y} (y z^{3}) = z^{3}

\frac{\partial}{\partial y} (z x^{3}) = 0

= x z + 3 x y^{2} + z^{3} + 0

Simplify

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

n = 1 \sum \infty (x - 4)^{n}

\frac{d}{d x} (ln (x x^{2} - 9))

x \to \infty lim (15)

f (x) = \frac{x}{x + 9}

\int x^{3} (2 x^{2} - 3) d x

What is (\partial)/(\partial y)(xyz+xy^3+yz^3+zx^3) ?
The answer to (\partial)/(\partial y)(xyz+xy^3+yz^3+zx^3) is xz+3xy^2+z^3