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

The answer to (\partial)/(\partial x)(2x^4yz^3) is 8x^3yz^3

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

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

8 x^{3} y z^{3}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 8 x^{3} y z^{3}

x \to 0 - lim (\frac{6}{5 x ^{\frac{1}{3}}})

\int (5 x^{2} - 2 x + 3) d x

x \to \infty lim (5 x + \frac{1}{x})

What is (\partial)/(\partial x)(2x^4yz^3) ?
The answer to (\partial)/(\partial x)(2x^4yz^3) is 8x^3yz^3