What is (\partial)/(\partial x)(x^{0.25}y^{0.75}) ?

The answer to (\partial)/(\partial x)(x^{0.25}y^{0.75}) is (0.25y^{0.75})/(x^{0.75)}

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(\partial)/(\partial x)(x^{0.25}y^{0.75})

\frac{\partial}{\partial x} (x^{0.25} y^{0.75})

\frac{0.25 y ^{0.75}}{x ^{0.75}}

Solution steps

\frac{\partial}{\partial x} (x^{0.25} y^{0.75})

Treat

y

as a constant

Take the constant out:

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

= y^{0.75} \frac{\partial}{\partial x} (x^{0.25})

Apply the Power Rule:

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

= y^{0.75} \cdot 0.25 x^{0.25 - 1}

Simplify

y^{0.75} \cdot 0.25 x^{0.25 - 1} : \frac{0.25 y ^{0.75}}{x ^{0.75}}

= \frac{0.25 y ^{0.75}}{x ^{0.75}}

y^{^{'}} + sin (t) y = sin (t), y (0) = 3

\int (- 2 y) d y

\frac{d y}{d x} = \frac{4}{x ^{2} e ^{3 y + 9}}

\frac{\partial}{\partial x} (x^{4} y^{3})

\int (\frac{x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}) d y

What is (\partial)/(\partial x)(x^{0.25}y^{0.75}) ?
The answer to (\partial)/(\partial x)(x^{0.25}y^{0.75}) is (0.25y^{0.75})/(x^{0.75)}