What is the derivative of \sin^{-1}(x)

Kathy Williams

Kathy Williams

Answered question

2021-12-17

What is the derivative of sin1(x)

Answer & Explanation

abonirali59

abonirali59

Beginner2021-12-18Added 35 answers

Let y=sin1(x)
Thus, sin(y)=x and π2yπ2
Now, diferentiate implicity
cos(y)dydx=1, so
dydx=1cos(y)
As we know, that π2yπ2, we understand that cos(y) is positive
dydx=11sin2(y)=11x2
Ethan Sanders

Ethan Sanders

Beginner2021-12-19Added 35 answers

sin1(x)=arcsin(x)
ddx(arcsin(x))
Apply the common derivative
=11x2

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