What is the derivative of x/(sqrt(4-x^2)) ?

The derivative of x/(sqrt(4-x^2)) is 4/((4-x^2)sqrt(4-x^2))

What is the first derivative of x/(sqrt(4-x^2)) ?

The first derivative of x/(sqrt(4-x^2)) is 4/((4-x^2)sqrt(4-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}{4 - x ^{2}})

\frac{4}{( 4 - x ^{2} ) 4 - x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d y}{d t} = y (3 - y), y (0) = 4

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

2 e^{t} + 5

\int 1 + 2 x^{2} + x^{4} d x

\frac{1}{x + 4}, 2

What is the derivative of x/(sqrt(4-x^2)) ?
The derivative of x/(sqrt(4-x^2)) is 4/((4-x^2)sqrt(4-x^2))
What is the first derivative of x/(sqrt(4-x^2)) ?
The first derivative of x/(sqrt(4-x^2)) is 4/((4-x^2)sqrt(4-x^2))