What is (\partial)/(\partial x)(x^{0.3}y^{0.7}) ?

The answer to (\partial)/(\partial x)(x^{0.3}y^{0.7}) is (0.3y^{0.7})/(x^{0.7)}

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(\partial)/(\partial x)(x^{0.3}y^{0.7})

\frac{\partial}{\partial x} (x^{0.3} y^{0.7})

\frac{0.3 y ^{0.7}}{x ^{0.7}}

Solution steps

\frac{\partial}{\partial x} (x^{0.3} y^{0.7})

Treat

y

as a constant

Take the constant out:

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

= y^{0.7} \frac{\partial}{\partial x} (x^{0.3})

Apply the Power Rule:

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

= y^{0.7} \cdot 0.3 x^{0.3 - 1}

Simplify

y^{0.7} \cdot 0.3 x^{0.3 - 1} : \frac{0.3 y ^{0.7}}{x ^{0.7}}

= \frac{0.3 y ^{0.7}}{x ^{0.7}}

What is (\partial)/(\partial x)(x^{0.3}y^{0.7}) ?
The answer to (\partial)/(\partial x)(x^{0.3}y^{0.7}) is (0.3y^{0.7})/(x^{0.7)}