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

The derivative of ((x^2+2)/(x^2-2))^4 is -(32x(x^2+2)^3)/((x^2-2)^5)

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

The first derivative of ((x^2+2)/(x^2-2))^4 is -(32x(x^2+2)^3)/((x^2-2)^5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

- \frac{32 x ( x ^{2} + 2 ) ^{3}}{( x ^{2} - 2 ) ^{5}}

Solution steps

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

Apply the chain rule:

4 (\frac{x ^{2} + 2}{x ^{2} - 2})^{3} \frac{d}{d x} (\frac{x ^{2} + 2}{x ^{2} - 2})

= 4 (\frac{x ^{2} + 2}{x ^{2} - 2})^{3} \frac{d}{d x} (\frac{x ^{2} + 2}{x ^{2} - 2})

\frac{d}{d x} (\frac{x ^{2} + 2}{x ^{2} - 2}) = - \frac{8 x}{( x ^{2} - 2 ) ^{2}}

= 4 (\frac{x ^{2} + 2}{x ^{2} - 2})^{3} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}})

Simplify

4 (\frac{x ^{2} + 2}{x ^{2} - 2})^{3} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}}) : - \frac{32 x ( x ^{2} + 2 ) ^{3}}{( x ^{2} - 2 ) ^{5}}

= - \frac{32 x ( x ^{2} + 2 ) ^{3}}{( x ^{2} - 2 ) ^{5}}

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

y = sin (x), y = cos (x)

(e^{, at})

\int x + 4 d x

\int p^{2} ln (p) d p

What is the derivative of ((x^2+2)/(x^2-2))^4 ?
The derivative of ((x^2+2)/(x^2-2))^4 is -(32x(x^2+2)^3)/((x^2-2)^5)
What is the first derivative of ((x^2+2)/(x^2-2))^4 ?
The first derivative of ((x^2+2)/(x^2-2))^4 is -(32x(x^2+2)^3)/((x^2-2)^5)