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}

e^{30 t}

f (x) = 3 x^{2} + 2 x, at x = - 2

\frac{d}{d t} (sin (6 t))

\int_{3}^{8} \frac{x + 1}{x} d x

y = 3 x^{2}, y = 6 - 3 x

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