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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(x + 10) (x - 10)

(1.5 \cdot 1 0^{3}) (2.4 \cdot 1 0^{14})

(e^{- 2 x}) (e^{- 2 x})

(x + 5)^{2} (x - 2)^{2}

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