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}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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}}}

1 - sin^{2} (x)

\int \frac{13 x e ^{2 x}}{( 1 + 2 x ) ^{2}} d x

\frac{\partial}{\partial x} (3 sin (x))

\int 4 x^{2} - sin (x) + 2 d x

(1 - \frac{4}{x + 2})^{3}

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}}