What is (\partial)/(\partial x)(x^{1/y}) ?

The answer to (\partial)/(\partial x)(x^{1/y}) is (x^{(1-y)/y})/(y)

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(\partial)/(\partial x)(x^{1/y})

\frac{\partial}{\partial x} (x^{\frac{1}{y}})

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

Solution steps

\frac{\partial}{\partial x} (x^{\frac{1}{y}})

Treat

y

as a constant

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{1}{5 x lo g _{7} ( x )} d x

x \to 6 - lim (f (x))

\frac{\partial ^{2}}{\partial x \partial y} (3 x y e^{- x^{2} y})

\frac{\partial}{\partial x} (\frac{x}{6 + y})

\int x \cdot x d x

What is (\partial)/(\partial x)(x^{1/y}) ?
The answer to (\partial)/(\partial x)(x^{1/y}) is (x^{(1-y)/y})/(y)