What is the derivative of Insqrt((x+1/(x-1))) ?

The derivative of Insqrt((x+1/(x-1))) is -(nI)/(sqrt(x+1)(x-1)^{3/2)}

What is the first derivative of Insqrt((x+1/(x-1))) ?

The first derivative of Insqrt((x+1/(x-1))) is -(nI)/(sqrt(x+1)(x-1)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (I n \frac{x + 1}{x - 1})

- \frac{n I}{x + 1 ( x - 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (I n \frac{x + 1}{x - 1})

Treat

n, I

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= I n \frac{d}{d x} (\frac{x + 1}{x - 1})

Apply the chain rule:

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

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

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

= I n \frac{1}{2 \frac{x + 1}{x - 1}} (- \frac{2}{( x - 1 ) ^{2}})

Simplify

I n \frac{1}{2 \frac{x + 1}{x - 1}} (- \frac{2}{( x - 1 ) ^{2}}) : - \frac{n I}{x + 1 ( x - 1 ) ^{\frac{3}{2}}}

= - \frac{n I}{x + 1 ( x - 1 ) ^{\frac{3}{2}}}

What is the derivative of Insqrt((x+1/(x-1))) ?
The derivative of Insqrt((x+1/(x-1))) is -(nI)/(sqrt(x+1)(x-1)^{3/2)}
What is the first derivative of Insqrt((x+1/(x-1))) ?
The first derivative of Insqrt((x+1/(x-1))) is -(nI)/(sqrt(x+1)(x-1)^{3/2)}