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

The derivative of (1+x^2/((1-x^2)^2)) is (2x(x^2+3))/((1-x^2)^3)

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

The first derivative of (1+x^2/((1-x^2)^2)) is (2x(x^2+3))/((1-x^2)^3)

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{1 + x ^{2}}{( 1 - x ^{2} ) ^{2}})

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((1 - x^{2})^{2}) = - 4 x (1 - x^{2})

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

Simplify

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

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

5 x^{\frac{7}{4}} + 5 x^{\frac{1}{3}} - 2

(2 x + t) \frac{d x}{d t} + x - 2 t = 0

\int e^{- \frac{x}{b}} d x

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

\frac{d}{d x} (20 x (1 - x)^{3})

What is the derivative of (1+x^2/((1-x^2)^2)) ?
The derivative of (1+x^2/((1-x^2)^2)) is (2x(x^2+3))/((1-x^2)^3)
What is the first derivative of (1+x^2/((1-x^2)^2)) ?
The first derivative of (1+x^2/((1-x^2)^2)) is (2x(x^2+3))/((1-x^2)^3)