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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

\frac{\partial}{\partial x} (x) = 1

= y^{\frac{1}{2}} \cdot 1

Simplify

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

y = \frac{x ^{5}}{10} + \frac{1}{6 x ^{3}}

n = 1 \sum \infty \frac{n}{( n + 1 ) !}

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\int \frac{e ^{4 x}}{e ^{4 x} + 1} d x

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