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

The answer to (\partial)/(\partial x)(2(y/x)^{1/2}) is -(y/(x^3))^{1/2}

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

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

- (\frac{y}{x ^{3}})^{\frac{1}{2}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

2 \cdot \frac{1}{2 ( \frac{y}{x} ) ^{\frac{1}{2}}} (- \frac{y}{x ^{2}}) : - (\frac{y}{x ^{3}})^{\frac{1}{2}}

= - (\frac{y}{x ^{3}})^{\frac{1}{2}}

f (x) = 3 x + 3

\frac{d ^{2}}{d x ^{2}} (k x)

n = 1 \sum \infty \frac{x ^{n}}{n \cdot 5 n}

\frac{d}{d x} ((x^{3} - 16 x)^{10})

\frac{d}{d t} (1 + t)

What is (\partial)/(\partial x)(2(y/x)^{1/2}) ?
The answer to (\partial)/(\partial x)(2(y/x)^{1/2}) is -(y/(x^3))^{1/2}