What is (\partial)/(\partial x)(2sqrt(y/x)) ?

The answer to (\partial)/(\partial x)(2sqrt(y/x)) is -sqrt(y/(x^3))

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(\partial)/(\partial x)(2sqrt(y/x))

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

- \frac{y}{x ^{3}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

Simplify

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

= - \frac{y}{x ^{3}}

x \to 0 lim (e^{4 x})

\frac{d x}{d t} = 6.4286 - 0.10714 x

y = 5^{x^{3}}

\frac{8 x}{x ^{2} - 1}

\int_{6}^{8} \frac{38}{( x - 6 ) ^{3}} d x

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