What is the derivative of x^{9/5}y^7z^{2/7} ?

The derivative of x^{9/5}y^7z^{2/7} is (9{y}^7{z}^{2/7)/x ^{4/5}}{5}

What is the first derivative of x^{9/5}y^7z^{2/7} ?

The first derivative of x^{9/5}y^7z^{2/7} is (9{y}^7{z}^{2/7)/x ^{4/5}}{5}

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\frac{d}{d x} (x^{\frac{9}{5}} y^{7} z^{\frac{2}{7}})

\frac{9 y ^{7} z ^{\frac{2}{7}} x ^{\frac{4}{5}}}{5}

Solution steps

\frac{d}{d x} (x^{\frac{9}{5}} y^{7} z^{\frac{2}{7}})

Take the constant out:

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

= y^{7} z^{\frac{2}{7}} \frac{d}{d x} (x^{\frac{9}{5}})

Apply the Power Rule:

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

= y^{7} z^{\frac{2}{7}} \frac{9}{5} x^{\frac{9}{5} - 1}

Simplify

y^{7} z^{\frac{2}{7}} \frac{9}{5} x^{\frac{9}{5} - 1} : \frac{9 y ^{7} z ^{\frac{2}{7}} x ^{\frac{4}{5}}}{5}

= \frac{9 y ^{7} z ^{\frac{2}{7}} x ^{\frac{4}{5}}}{5}

What is the derivative of x^{9/5}y^7z^{2/7} ?
The derivative of x^{9/5}y^7z^{2/7} is (9{y}^7{z}^{2/7)/x ^{4/5}}{5}
What is the first derivative of x^{9/5}y^7z^{2/7} ?
The first derivative of x^{9/5}y^7z^{2/7} is (9{y}^7{z}^{2/7)/x ^{4/5}}{5}