What is the derivative of arcsin(1/t) ?

The derivative of arcsin(1/t) is -(sqrt(t^2))/(t^2sqrt(t^2-1))

What is the first derivative of arcsin(1/t) ?

The first derivative of arcsin(1/t) is -(sqrt(t^2))/(t^2sqrt(t^2-1))

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derivative of

arcsin (\frac{1}{t})

- \frac{t ^{2}}{t ^{2} t ^{2} - 1}

Solution steps

\frac{d}{d t} (arcsin (\frac{1}{t}))

Apply the chain rule:

\frac{1}{1 - ( \frac{1}{t} ) ^{2}} \frac{d}{d t} (\frac{1}{t})

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

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

= \frac{1}{1 - ( \frac{1}{t} ) ^{2}} (- \frac{1}{t ^{2}})

Simplify

\frac{1}{1 - ( \frac{1}{t} ) ^{2}} (- \frac{1}{t ^{2}}) : - \frac{t ^{2}}{t ^{2} t ^{2} - 1}

= - \frac{t ^{2}}{t ^{2} t ^{2} - 1}

What is the derivative of arcsin(1/t) ?
The derivative of arcsin(1/t) is -(sqrt(t^2))/(t^2sqrt(t^2-1))
What is the first derivative of arcsin(1/t) ?
The first derivative of arcsin(1/t) is -(sqrt(t^2))/(t^2sqrt(t^2-1))