What is (\partial)/(\partial y)((z)(3x^2y+4xy^2)) ?

The answer to (\partial)/(\partial y)((z)(3x^2y+4xy^2)) is z(3x^2+8xy)

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(\partial)/(\partial y)((z)(3x^2y+4xy^2))

\frac{\partial}{\partial y} ((z) (3 x^{2} y + 4 x y^{2}))

z (3 x^{2} + 8 x y)

Solution steps

\frac{\partial}{\partial y} ((z) (3 x^{2} y + 4 x y^{2}))

Treat

z, x

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial y} (3 x^{2} y + 4 x y^{2})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial y} (3 x^{2} y) + \frac{\partial}{\partial y} (4 x y^{2}))

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

\frac{\partial}{\partial y} (4 x y^{2}) = 8 x y

= z (3 x^{2} + 8 x y)

(- 2 b - 3 c)^{2}

\frac{4 ( x - 3 )}{x + 3}

x i \cdot (x i + 1) \cdot (x i + 3)

e^{x} \times (5 x^{2} - 3)

\frac{d}{d y} ((x) (6 x^{3} + 2 x + 9))

What is (\partial)/(\partial y)((z)(3x^2y+4xy^2)) ?
The answer to (\partial)/(\partial y)((z)(3x^2y+4xy^2)) is z(3x^2+8xy)