What is the derivative of (x^2)/(1+x^2) ?

The derivative of (x^2)/(1+x^2) is (2x)/((1+x^2)^2)

What is the first derivative of (x^2)/(1+x^2) ?

The first derivative of (x^2)/(1+x^2) is (2x)/((1+x^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{x ^{2}}{1 + x ^{2}}

\frac{2 x}{( 1 + x ^{2} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (1 + x^{2}) = 2 x

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

Simplify

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

= \frac{2 x}{( 1 + x ^{2} ) ^{2}}

What is the derivative of (x^2)/(1+x^2) ?
The derivative of (x^2)/(1+x^2) is (2x)/((1+x^2)^2)
What is the first derivative of (x^2)/(1+x^2) ?
The first derivative of (x^2)/(1+x^2) is (2x)/((1+x^2)^2)