What is the derivative of ({f}(x)/x) ?

The derivative of ({f}(x)/x) is (x derivative of {f}(x)-{f}(x))/(x^2)

What is the first derivative of ({f}(x)/x) ?

The first derivative of ({f}(x)/x) is (x derivative of {f}(x)-{f}(x))/(x^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{f ( x )}{x})

\frac{x \frac{d}{d x} ( f ( x ) ) - f ( x )}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

= \frac{\frac{d}{d x} ( f ( x ) ) x - 1 \cdot f ( x )}{x ^{2}}

Simplify

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

What is the derivative of ({f}(x)/x) ?
The derivative of ({f}(x)/x) is (x derivative of {f}(x)-{f}(x))/(x^2)
What is the first derivative of ({f}(x)/x) ?
The first derivative of ({f}(x)/x) is (x derivative of {f}(x)-{f}(x))/(x^2)