Best solutions to - "What is the derivative of sin−1(x)"

Kathy Williams

Answered question

2021-12-17

What is the derivative of

\sin^{- 1} (x)

abonirali59

Beginner2021-12-18Added 35 answers

Let

y = \sin^{- 1} (x)

Thus,

\sin (y) = x

and

- \frac{π}{2} \leq y \leq \frac{π}{2}

Now, diferentiate implicity

\cos (y) \frac{d y}{d x} = 1

, so

\frac{d y}{d x} = \frac{1}{\cos (y)}

As we know, that

- \frac{π}{2} \leq y \leq \frac{π}{2}

, we understand that

\cos (y)

is positive

\frac{d y}{d x} = \frac{1}{\sqrt{1 - \sin^{2} (y)}} = \frac{1}{\sqrt{1 - x^{2}}}

Ethan Sanders

Beginner2021-12-19Added 35 answers

\sin^{- 1} (x) = \arcsin (x)

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

Apply the common derivative

= \frac{1}{\sqrt{1 - x^{2}}}

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