What is the derivative of ((x^2+1/(x^2-1))^8) ?

The derivative of ((x^2+1/(x^2-1))^8) is -(32x(x^2+1)^7)/((x^2-1)^9)

What is the first derivative of ((x^2+1/(x^2-1))^8) ?

The first derivative of ((x^2+1/(x^2-1))^8) is -(32x(x^2+1)^7)/((x^2-1)^9)

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 ^{2} + 1}{x ^{2} - 1})^{8})

- \frac{32 x ( x ^{2} + 1 ) ^{7}}{( x ^{2} - 1 ) ^{9}}

Solution steps

\frac{d}{d x} ((\frac{x ^{2} + 1}{x ^{2} - 1})^{8})

Apply the chain rule:

8 (\frac{x ^{2} + 1}{x ^{2} - 1})^{7} \frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 1})

= 8 (\frac{x ^{2} + 1}{x ^{2} - 1})^{7} \frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 1})

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

= 8 (\frac{x ^{2} + 1}{x ^{2} - 1})^{7} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}})

Simplify

8 (\frac{x ^{2} + 1}{x ^{2} - 1})^{7} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}}) : - \frac{32 x ( x ^{2} + 1 ) ^{7}}{( x ^{2} - 1 ) ^{9}}

= - \frac{32 x ( x ^{2} + 1 ) ^{7}}{( x ^{2} - 1 ) ^{9}}

\frac{\partial}{\partial x} (x^{5} + x y^{7} + 4)

x \to - 3 - lim (4 x^{2} - 6 x + 3)

x \to 3 lim (\frac{ln ( 3 - x )}{x - 2})

\frac{d}{d x} ((ln (x))^{l n (x)})

x \to 7 lim (\frac{x + 4}{x - 7})

What is the derivative of ((x^2+1/(x^2-1))^8) ?
The derivative of ((x^2+1/(x^2-1))^8) is -(32x(x^2+1)^7)/((x^2-1)^9)
What is the first derivative of ((x^2+1/(x^2-1))^8) ?
The first derivative of ((x^2+1/(x^2-1))^8) is -(32x(x^2+1)^7)/((x^2-1)^9)