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

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

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

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

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

Solution steps

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

Simplify

(z) (x^{2} x y^{2} z) : z^{2} x^{3} y^{2}

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

Treat

z, x

as constants

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= z^{2} x^{3} \cdot 2 y^{2 - 1}

Simplify

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

\frac{5}{2}^{2}

16 - x^{2} \cdot x + 1

e^{(- 4)}

e^{(- 2)}

k^{0.5} \cdot (4 k)^{0.5}

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