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

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

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

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

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

Solution steps

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

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}}

f (x) = 9 e^{5} x + e^{- x^{2}}, at x = 1

\frac{d y}{d x} = 6 x^{2} y^{2}

x \to 2 - lim (4 - x^{2})

f (r) = \frac{5}{r ^{3}}

\frac{d}{d x} (2 x y + y)

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