What is the derivative of y=arcsin((x+1)/(x-1)) ?

The derivative of y=arcsin((x+1)/(x-1)) is -2/(sqrt(-\frac{4x){(x-1)^2)}(x-1)^2}

What is the first derivative of y=arcsin((x+1)/(x-1)) ?

The first derivative of y=arcsin((x+1)/(x-1)) is -2/(sqrt(-\frac{4x){(x-1)^2)}(x-1)^2}

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derivative of

y = arcsin (\frac{x + 1}{x - 1})

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

Solution steps

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

Apply the chain rule:

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

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

Simplify

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

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

What is the derivative of y=arcsin((x+1)/(x-1)) ?
The derivative of y=arcsin((x+1)/(x-1)) is -2/(sqrt(-\frac{4x){(x-1)^2)}(x-1)^2}
What is the first derivative of y=arcsin((x+1)/(x-1)) ?
The first derivative of y=arcsin((x+1)/(x-1)) is -2/(sqrt(-\frac{4x){(x-1)^2)}(x-1)^2}