What is (\partial)/(\partial y)(-xy^2z+4xy) ?

The answer to (\partial)/(\partial y)(-xy^2z+4xy) is -2xzy+4x

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(\partial)/(\partial y)(-xy^2z+4xy)

\frac{\partial}{\partial y} (- x y^{2} z + 4 x y)

- 2 x zy + 4 x

Solution steps

\frac{\partial}{\partial y} (- x y^{2} z + 4 x y)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial y} (x y^{2} z) + \frac{\partial}{\partial y} (4 x y)

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

\frac{\partial}{\partial y} (4 x y) = 4 x

= - 2 x zy + 4 x

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

\int \frac{3}{x ^{3} + x} d x

\int_{0}^{2} t e^{2 t} d t

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

\int (\frac{x}{x x ^{2} + 36}) d x

What is (\partial)/(\partial y)(-xy^2z+4xy) ?
The answer to (\partial)/(\partial y)(-xy^2z+4xy) is -2xzy+4x