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

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

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

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

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

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

Solution steps

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

Simplify

\frac{x + 1}{x - 1} : \frac{x + 1}{x - 1}

= \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}}

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

Simplify

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

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

\frac{d}{d x} (x^{x^{x}})

x \to \infty lim (\frac{2 ^{- x} - 2 ^{x}}{2 ^{- x} + 2 ^{x}})

\int \frac{2 x}{3 x ^{2} - 4} d x

\frac{3}{5 + x ^{2}}

n = 1 \sum \infty (\frac{- 2}{3})^{n}

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