What is (\partial)/(\partial y)(5x^2-3xy^2+xyz) ?

The answer to (\partial)/(\partial y)(5x^2-3xy^2+xyz) is xz-6xy

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(\partial)/(\partial y)(5x^2-3xy^2+xyz)

\frac{\partial}{\partial y} (5 x^{2} - 3 x y^{2} + x yz)

x z - 6 x y

Solution steps

\frac{\partial}{\partial y} (5 x^{2} - 3 x y^{2} + x yz)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (5 x^{2}) - \frac{\partial}{\partial y} (3 x y^{2}) + \frac{\partial}{\partial y} (x yz)

\frac{\partial}{\partial y} (5 x^{2}) = 0

\frac{\partial}{\partial y} (3 x y^{2}) = 6 x y

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

= 0 - 6 x y + x z

Simplify

= x z - 6 x y

n \to \infty lim (2 n)

x \to \infty lim (\frac{2 x ^{2}}{- x + 2})

\frac{x}{1 + 4 x ^{2}}, 6

\frac{\partial}{\partial x} (in x y)

\int \frac{y ^{2}}{16} d y

What is (\partial)/(\partial y)(5x^2-3xy^2+xyz) ?
The answer to (\partial)/(\partial y)(5x^2-3xy^2+xyz) is xz-6xy