What is (\partial)/(\partial x)(ax^by^{(1-b)}) ?

The answer to (\partial)/(\partial x)(ax^by^{(1-b)}) is ay^{1-b}bx^{b-1}

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(\partial)/(\partial x)(ax^by^{(1-b)})

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

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

Solution steps

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

Treat

a, b, y

as constants

Take the constant out:

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

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

Apply the Power Rule:

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

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

What is (\partial)/(\partial x)(ax^by^{(1-b)}) ?
The answer to (\partial)/(\partial x)(ax^by^{(1-b)}) is ay^{1-b}bx^{b-1}