What is the derivative of ((x^2+2)/(x^2-2))^5 ?

The derivative of ((x^2+2)/(x^2-2))^5 is -(40x(x^2+2)^4)/((x^2-2)^6)

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

The first derivative of ((x^2+2)/(x^2-2))^5 is -(40x(x^2+2)^4)/((x^2-2)^6)

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})^{5}

- \frac{40 x ( x ^{2} + 2 ) ^{4}}{( x ^{2} - 2 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

= 5 (\frac{x ^{2} + 2}{x ^{2} - 2})^{4} \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}}

= 5 (\frac{x ^{2} + 2}{x ^{2} - 2})^{4} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}})

Simplify

5 (\frac{x ^{2} + 2}{x ^{2} - 2})^{4} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}}) : - \frac{40 x ( x ^{2} + 2 ) ^{4}}{( x ^{2} - 2 ) ^{6}}

= - \frac{40 x ( x ^{2} + 2 ) ^{4}}{( x ^{2} - 2 ) ^{6}}

\frac{d}{d x} (\frac{1}{3 x ^{2} - 1})

20 x - 16 x^{2}

y^{^{''}} + 16 y = 3 csc^{2} (4 t)

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

\frac{d y}{d x} = 1 + y + x^{2} + y x^{2}

What is the derivative of ((x^2+2)/(x^2-2))^5 ?
The derivative of ((x^2+2)/(x^2-2))^5 is -(40x(x^2+2)^4)/((x^2-2)^6)
What is the first derivative of ((x^2+2)/(x^2-2))^5 ?
The first derivative of ((x^2+2)/(x^2-2))^5 is -(40x(x^2+2)^4)/((x^2-2)^6)