What is the d/(d{x)}({x}^{({y})/({z)}}) ?

The d/(d{x)}({x}^{({y})/({z)}}) is ({y)/x ^{({y}-{z})/({z)}}}{{z}}

What is the first d/(d{x)}({x}^{({y})/({z)}}) ?

The first d/(d{x)}({x}^{({y})/({z)}}) is ({y)/x ^{({y}-{z})/({z)}}}{{z}}

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\frac{d}{d x} (x^{\frac{y}{z}})

\frac{y x ^{\frac{y - z}{z}}}{z}

Solution steps

\frac{d}{d x} (x^{\frac{y}{z}})

Apply the Power Rule:

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

= \frac{y}{z} x^{\frac{y}{z} - 1}

Simplify

\frac{y}{z} x^{\frac{y}{z} - 1} : \frac{y x ^{\frac{y - z}{z}}}{z}

= \frac{y x ^{\frac{y - z}{z}}}{z}

What is the d/(d{x)}({x}^{({y})/({z)}}) ?
The d/(d{x)}({x}^{({y})/({z)}}) is ({y)/x ^{({y}-{z})/({z)}}}{{z}}
What is the first d/(d{x)}({x}^{({y})/({z)}}) ?
The first d/(d{x)}({x}^{({y})/({z)}}) is ({y)/x ^{({y}-{z})/({z)}}}{{z}}