What is (\partial)/(\partial x)(2x^{1/2}y^{1/4}) ?

The answer to (\partial)/(\partial x)(2x^{1/2}y^{1/4}) is (y^{1/4})/(x^{1/2)}

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(\partial)/(\partial x)(2x^{1/2}y^{1/4})

\frac{\partial}{\partial x} (2 x^{\frac{1}{2}} y^{\frac{1}{4}})

\frac{y ^{\frac{1}{4}}}{x ^{\frac{1}{2}}}

Solution steps

\frac{\partial}{\partial x} (2 x^{\frac{1}{2}} y^{\frac{1}{4}})

Treat

y

as a constant

Take the constant out:

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

= 2 y^{\frac{1}{4}} \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 2 y^{\frac{1}{4}} \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

2 y^{\frac{1}{4}} \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{y ^{\frac{1}{4}}}{x ^{\frac{1}{2}}}

= \frac{y ^{\frac{1}{4}}}{x ^{\frac{1}{2}}}

x^{3} - \frac{x ^{2}}{40}

y^{^{'}} = 4 + 2 sin (\frac{x}{4}) - \frac{y}{100}

\int \frac{1}{n ( ln ( n ) ) ^{2}}

\int_{0}^{1} (3 - 4 x) e^{2 x} d x

y^{^{''}} + \frac{200}{8} \cdot y = 30 sin (2 x), y (0) = 2, y^{^{'}} (0) = 0

What is (\partial)/(\partial x)(2x^{1/2}y^{1/4}) ?
The answer to (\partial)/(\partial x)(2x^{1/2}y^{1/4}) is (y^{1/4})/(x^{1/2)}