What is (\partial)/(\partial y)(8xy^2z^3) ?

The answer to (\partial)/(\partial y)(8xy^2z^3) is 16xyz^3

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(\partial)/(\partial y)(8xy^2z^3)

\frac{\partial}{\partial y} (8 x y^{2} z^{3})

16 x y z^{3}

Solution steps

\frac{\partial}{\partial y} (8 x y^{2} z^{3})

Treat

x, z

as constants

Take the constant out:

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

= 8 x z^{3} \frac{\partial}{\partial y} (y^{2})

Apply the Power Rule:

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

= 8 x z^{3} \cdot 2 y^{2 - 1}

Simplify

= 16 x y z^{3}

\int_{0}^{2} sin (x) d x

\int \frac{- 5 x + 2}{( x + 1 ) ^{2}} d x

\frac{d}{d x} (cos (x - \frac{π}{6}))

y^{^{'}} = y e^{x}

y = (1 - 5 x)^{6}

What is (\partial)/(\partial y)(8xy^2z^3) ?
The answer to (\partial)/(\partial y)(8xy^2z^3) is 16xyz^3