What is (\partial)/(\partial x)(5x^{y/z}) ?

The answer to (\partial)/(\partial x)(5x^{y/z}) is (5yx^{(y-z)/z})/(z)

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(\partial)/(\partial x)(5x^{y/z})

\frac{\partial}{\partial x} (5 x^{\frac{y}{z}})

\frac{5 y x ^{\frac{y - z}{z}}}{z}

Solution steps

\frac{\partial}{\partial x} (5 x^{\frac{y}{z}})

Treat

y, z

as constants

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (x^{\frac{y}{z}})

Apply the Power Rule:

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

= 5 \cdot \frac{y}{z} x^{\frac{y}{z} - 1}

Simplify

5 \cdot \frac{y}{z} x^{\frac{y}{z} - 1} : \frac{5 y x ^{\frac{y - z}{z}}}{z}

= \frac{5 y x ^{\frac{y - z}{z}}}{z}

x y^{^{'}} = y + 7 x^{2} sin (x), y (π) = 0

x \to 1 lim (5 x + 6)

\frac{d}{d x} (- 3^{- 2} (tan (7 x))^{5})

(2 cos (x))^{^{'}}

y^{2} = x - 2, y = x - 4

What is (\partial)/(\partial x)(5x^{y/z}) ?
The answer to (\partial)/(\partial x)(5x^{y/z}) is (5yx^{(y-z)/z})/(z)