What is (\partial)/(\partial z)(2x^4yz^3) ?

The answer to (\partial)/(\partial z)(2x^4yz^3) is 6x^4yz^2

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(\partial)/(\partial z)(2x^4yz^3)

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

6 x^{4} y z^{2}

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

= 2 x^{4} y \cdot 3 z^{3 - 1}

Simplify

= 6 x^{4} y z^{2}

\frac{d}{d x} (\frac{3}{4 x ^{8}})

x y^{^{'}} + y = 6 x y^{2}, y (1) = - 4

1 - 2 sin^{3} (x)

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

\frac{d}{d x} (\frac{4 x ^{5} + 6}{x ^{3}})

What is (\partial)/(\partial z)(2x^4yz^3) ?
The answer to (\partial)/(\partial z)(2x^4yz^3) is 6x^4yz^2