What is (\partial)/(\partial x)(x^zy^{1-z}) ?

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

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(\partial)/(\partial x)(x^zy^{1-z})

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

y^{1 - z} z x^{z - 1}

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

= y^{1 - z} \frac{\partial}{\partial x} (x^{z})

Apply the Power Rule:

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

= y^{1 - z} z x^{z - 1}

- 3 e^{x + 4} + e^{3}

f (x) = (x^{2} - 18) (2 x - 3)

\frac{d}{d x} (\frac{- x ^{3}}{y ^{3}})

\int t e^{a t} d t

n = 0 \sum \infty \frac{8}{n} - \frac{8}{n + 1}

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