What is (\partial)/(\partial y)(x^2y+y^2z) ?

The answer to (\partial)/(\partial y)(x^2y+y^2z) is x^2+2zy

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(\partial)/(\partial y)(x^2y+y^2z)

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

x^{2} + 2 zy

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= x^{2} + 2 zy

\frac{d}{d x} (\frac{1}{x ( x + 1 )})

\int (3 t + 3)^{2.2} d t

y = 6 x - 11

\int (\frac{5}{x} + sec^{2} (x)) d x

x \to 2 lim (3.5 + 5.6)

What is (\partial)/(\partial y)(x^2y+y^2z) ?
The answer to (\partial)/(\partial y)(x^2y+y^2z) is x^2+2zy