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 >

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

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

Solution steps

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

Take the constant out:

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

= - \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 13 - x^{2} d x

\frac{\partial}{\partial z} (2 y sin (x) + e^{2 z})

\int_{\frac{1}{5}}^{3} 14 x ln (5 x) d x

\frac{d}{d x} (d u (d, x))

\int x^{2} sec^{2} (3 x^{3}) d x

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))