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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

f (x) = x^{π}

\frac{d x}{d y} = x

\int (\frac{t ^{3}}{3} + \frac{1}{4 t ^{2}}) d t

\frac{\partial}{\partial x} (- 3 sin (4 x))

t - 4

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