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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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