What is (\partial)/(\partial x)(4sqrt(y/x)) ?

The answer to (\partial)/(\partial x)(4sqrt(y/x)) is -(2sqrt(y))/(x^{3/2)}

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(\partial)/(\partial x)(4sqrt(y/x))

\frac{\partial}{\partial x} (4 \frac{y}{x})

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

Solution steps

\frac{\partial}{\partial x} (4 \frac{y}{x})

Treat

y

as a constant

Take the constant out:

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

= 4 \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}}

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

Simplify

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

= - \frac{2 y}{x ^{\frac{3}{2}}}

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

y = (x)

y = 4 x - 16, y^{2} = 4 x + 4

y = arctan (7 x^{2} - 1)

\int x (cos^{2} (x)) d x

What is (\partial)/(\partial x)(4sqrt(y/x)) ?
The answer to (\partial)/(\partial x)(4sqrt(y/x)) is -(2sqrt(y))/(x^{3/2)}