What is (\partial)/(\partial x)(x^ay^{1-a}) ?

The answer to (\partial)/(\partial x)(x^ay^{1-a}) is y^{1-a}ax^{a-1}

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(\partial)/(\partial x)(x^ay^{1-a})

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

y^{1 - a} a x^{a - 1}

Solution steps

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

Treat

a, y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

\frac{\partial}{\partial x} (sin (x + 2 y))

\int_{- 1}^{1} x (x^{2} + 3)^{3} d x

x \to - 2 - lim (\frac{3 x - 6}{x + 2})

\frac{d}{d x} (\frac{π}{4} x)

\int \frac{sec ( θ ) tan ( θ )}{1 + sec ( θ )} d θ

What is (\partial)/(\partial x)(x^ay^{1-a}) ?
The answer to (\partial)/(\partial x)(x^ay^{1-a}) is y^{1-a}ax^{a-1}