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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

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}

35.4 cos (0.1 (x + 6.2))

x \to 1.01 lim (\frac{1}{x ^{2} - 1})

\frac{d}{d x} (1 + 3 x + 9 x^{2})

f (x) = 5 x^{2}

(9 x^{2} + y - 1) d x - (14 y - x) d y = 0, y (1) = 0

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