What is the derivative of 1/(4-x^2) ?

The derivative of 1/(4-x^2) is (2x)/((4-x^2)^2)

What is the first derivative of 1/(4-x^2) ?

The first derivative of 1/(4-x^2) is (2x)/((4-x^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{1}{4 - x ^{2}}

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of 1/(4-x^2) ?
The derivative of 1/(4-x^2) is (2x)/((4-x^2)^2)
What is the first derivative of 1/(4-x^2) ?
The first derivative of 1/(4-x^2) is (2x)/((4-x^2)^2)