What is (\partial)/(\partial x)(x^8y) ?

The answer to (\partial)/(\partial x)(x^8y) is 8x^7y

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(\partial)/(\partial x)(x^8y)

\frac{\partial}{\partial x} (x^{8} y)

8 x^{7} y

Solution steps

\frac{\partial}{\partial x} (x^{8} y)

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= y \cdot 8 x^{8 - 1}

Simplify

= 8 x^{7} y

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\int_{1}^{\infty} 6 e^{- 2 x} d x

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What is (\partial)/(\partial x)(x^8y) ?
The answer to (\partial)/(\partial x)(x^8y) is 8x^7y