What is (\partial)/(\partial x)(1/4 x^ay^{1-a}) ?

The answer to (\partial)/(\partial x)(1/4 x^ay^{1-a}) is (ax^{a-1}y^{1-a})/4

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(\partial)/(\partial x)(1/4 x^ay^{1-a})

\frac{\partial}{\partial x} (\frac{1}{4} x^{a} y^{1 - a})

\frac{a x ^{a - 1} y ^{1 - a}}{4}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{4} x^{a} y^{1 - a})

Treat

a, y

as a constant

Take the constant out:

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

= \frac{1}{4} y^{1 - a} \frac{\partial}{\partial x} (x^{a})

Apply the Power Rule:

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

= \frac{1}{4} y^{1 - a} a x^{a - 1}

Simplify

\frac{1}{4} y^{1 - a} a x^{a - 1} : \frac{a x ^{a - 1} y ^{1 - a}}{4}

= \frac{a x ^{a - 1} y ^{1 - a}}{4}

\int e^{- 2} d x

4 x - 12, [2, 6]

\int e^{2 \cdot x} d x

(x^{12} - 1)^{3}

\int \frac{7 x ^{3} + x ^{2}}{x} d x

What is (\partial)/(\partial x)(1/4 x^ay^{1-a}) ?
The answer to (\partial)/(\partial x)(1/4 x^ay^{1-a}) is (ax^{a-1}y^{1-a})/4