What is (\partial)/(\partial x)(5x^3yz^2) ?

The answer to (\partial)/(\partial x)(5x^3yz^2) is 15x^2yz^2

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(\partial)/(\partial x)(5x^3yz^2)

\frac{\partial}{\partial x} (5 x^{3} y z^{2})

15 x^{2} y z^{2}

Solution steps

\frac{\partial}{\partial x} (5 x^{3} y z^{2})

Treat

y, z

as constants

Take the constant out:

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

= 5 y z^{2} \frac{\partial}{\partial x} (x^{3})

Apply the Power Rule:

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

= 5 y z^{2} \cdot 3 x^{3 - 1}

Simplify

= 15 x^{2} y z^{2}

\int_{- 1}^{2} x^{3} - 1 d x

x \to 0 lim (x^{4})

\int x^{2} cos (5 x) d x

f (x) = 2 sin (x), (\frac{π}{6}, 1)

What is (\partial)/(\partial x)(5x^3yz^2) ?
The answer to (\partial)/(\partial x)(5x^3yz^2) is 15x^2yz^2