What is (\partial)/(\partial x)(6x^{y/z}) ?

The answer to (\partial)/(\partial x)(6x^{y/z}) is (6yx^{(y-z)/z})/(z)

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(\partial)/(\partial x)(6x^{y/z})

\frac{\partial}{\partial x} (6 x^{\frac{y}{z}})

\frac{6 y x ^{\frac{y - z}{z}}}{z}

Solution steps

\frac{\partial}{\partial x} (6 x^{\frac{y}{z}})

Treat

y, z

as constants

Take the constant out:

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

= 6 \frac{\partial}{\partial x} (x^{\frac{y}{z}})

Apply the Power Rule:

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

= 6 \cdot \frac{y}{z} x^{\frac{y}{z} - 1}

Simplify

6 \cdot \frac{y}{z} x^{\frac{y}{z} - 1} : \frac{6 y x ^{\frac{y - z}{z}}}{z}

= \frac{6 y x ^{\frac{y - z}{z}}}{z}

\frac{d}{d x} (x^{2} - 2 x e^{- x} + e^{- 2 x})

\int_{0}^{2} ∣ x ∣ d x

x \to 0 lim (x (e^{x} - \frac{1}{x}))

f (x) = x^{2} + 3 x - 3, at x = 1

f (t) = e^{5 t s i n (2 t)}

What is (\partial)/(\partial x)(6x^{y/z}) ?
The answer to (\partial)/(\partial x)(6x^{y/z}) is (6yx^{(y-z)/z})/(z)