What is (\partial)/(\partial x)(x^{4/7}y^{1/7}z^{2/7}) ?

The answer to (\partial)/(\partial x)(x^{4/7}y^{1/7}z^{2/7}) is (4y^{1/7}z^{2/7})/(7x^{3/7)}

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(\partial)/(\partial x)(x^{4/7}y^{1/7}z^{2/7})

\frac{\partial}{\partial x} (x^{\frac{4}{7}} y^{\frac{1}{7}} z^{\frac{2}{7}})

\frac{4 y ^{\frac{1}{7}} z ^{\frac{2}{7}}}{7 x ^{\frac{3}{7}}}

Solution steps

\frac{\partial}{\partial x} (x^{\frac{4}{7}} y^{\frac{1}{7}} z^{\frac{2}{7}})

Treat

y, z

as constants

Take the constant out:

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

= y^{\frac{1}{7}} z^{\frac{2}{7}} \frac{\partial}{\partial x} (x^{\frac{4}{7}})

Apply the Power Rule:

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

= y^{\frac{1}{7}} z^{\frac{2}{7}} \frac{4}{7} x^{\frac{4}{7} - 1}

Simplify

y^{\frac{1}{7}} z^{\frac{2}{7}} \frac{4}{7} x^{\frac{4}{7} - 1} : \frac{4 y ^{\frac{1}{7}} z ^{\frac{2}{7}}}{7 x ^{\frac{3}{7}}}

= \frac{4 y ^{\frac{1}{7}} z ^{\frac{2}{7}}}{7 x ^{\frac{3}{7}}}

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What is (\partial)/(\partial x)(x^{4/7}y^{1/7}z^{2/7}) ?
The answer to (\partial)/(\partial x)(x^{4/7}y^{1/7}z^{2/7}) is (4y^{1/7}z^{2/7})/(7x^{3/7)}