What is (\partial)/(\partial x)(5sqrt(y/x)) ?

The answer to (\partial)/(\partial x)(5sqrt(y/x)) is -(5sqrt(y))/(2x^{3/2)}

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(\partial)/(\partial x)(5sqrt(y/x))

\frac{\partial}{\partial x} (5 \frac{y}{x})

- \frac{5 y}{2 x ^{\frac{3}{2}}}

Solution steps

\frac{\partial}{\partial x} (5 \frac{y}{x})

Treat

y

as a constant

Take the constant out:

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

= 5 \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}}

= 5 \cdot \frac{1}{2 \frac{y}{x}} (- \frac{y}{x ^{2}})

Simplify

5 \cdot \frac{1}{2 \frac{y}{x}} (- \frac{y}{x ^{2}}) : - \frac{5 y}{2 x ^{\frac{3}{2}}}

= - \frac{5 y}{2 x ^{\frac{3}{2}}}

x \to 0 - lim (\frac{x}{3 x ^{4} - 15 x})

f (x) = (1 - x) (x^{2} - 3) 2, (2, - 1)

\int_{0}^{π} π (3 sin^{2} (x))^{2} d x

\frac{\partial}{\partial z} (e^{x y} \cdot sin (z))

x \to 0 lim (\frac{3}{x ^{3}})

What is (\partial)/(\partial x)(5sqrt(y/x)) ?
The answer to (\partial)/(\partial x)(5sqrt(y/x)) is -(5sqrt(y))/(2x^{3/2)}