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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int x^{2} e^{2 x^{3}} d x

x \to + 6 lim (8)

\int \frac{ln ^{3} ( x )}{x ^{2}} d x

\frac{d y}{d x} = - 2 y + x

x^{\frac{1}{5}}

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