What is (\partial)/(\partial x)(x^5y^5) ?

The answer to (\partial)/(\partial x)(x^5y^5) is 5x^4y^5

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(\partial)/(\partial x)(x^5y^5)

\frac{\partial}{\partial x} (x^{5} y^{5})

5 x^{4} y^{5}

Solution steps

\frac{\partial}{\partial x} (x^{5} y^{5})

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= y^{5} \cdot 5 x^{5 - 1}

Simplify

= 5 x^{4} y^{5}

What is (\partial)/(\partial x)(x^5y^5) ?
The answer to (\partial)/(\partial x)(x^5y^5) is 5x^4y^5