What is the derivative of-x/(5y) ?

The derivative of-x/(5y) is -(y-x\frac{dy)/(dx)}{5y^2}

What is the first derivative of-x/(5y) ?

The first derivative of-x/(5y) is -(y-x\frac{dy)/(dx)}{5y^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (- \frac{x}{5 y})

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

Solution steps

\frac{d}{d x} (- \frac{x}{5 y})

Take the constant out:

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

= - \frac{1}{5} \frac{d}{d x} (\frac{x}{y})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

Simplify

- \frac{1}{5} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}} : - \frac{y - x \frac{d y}{d x}}{5 y ^{2}}

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

What is the derivative of-x/(5y) ?
The derivative of-x/(5y) is -(y-x\frac{dy)/(dx)}{5y^2}
What is the first derivative of-x/(5y) ?
The first derivative of-x/(5y) is -(y-x\frac{dy)/(dx)}{5y^2}