What is the derivative of sqrt(y/x) ?

The derivative of sqrt(y/x) is (x\frac{dy)/(dx)-y}{2x^{3/2}sqrt(y)}

What is the first derivative of sqrt(y/x) ?

The first derivative of sqrt(y/x) is (x\frac{dy)/(dx)-y}{2x^{3/2}sqrt(y)}

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Popular >

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

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

Solution steps

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

Apply the chain rule:

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

= \frac{1}{2 \frac{y}{x}} \frac{d}{d x} (\frac{y}{x})

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

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

Simplify

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

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

- 1.5 e^{- 1.5} 3

(1.992 \cdot 1 0^{- 5}) 28.01

x^{- 3} (x^{6} \cdot e^{3 x})

567 e^{- 3 (0)}

7 e^{- 0.093 \cdot 32}

What is the derivative of sqrt(y/x) ?
The derivative of sqrt(y/x) is (x\frac{dy)/(dx)-y}{2x^{3/2}sqrt(y)}
What is the first derivative of sqrt(y/x) ?
The first derivative of sqrt(y/x) is (x\frac{dy)/(dx)-y}{2x^{3/2}sqrt(y)}