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

Kathy Williams 2021-12-17 Answered
What is the derivative of sin1(x)
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Expert Answer

abonirali59
Answered 2021-12-18 Author has 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
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Ethan Sanders
Answered 2021-12-19 Author has 35 answers
sin1(x)=arcsin(x)
ddx(arcsin(x))
Apply the common derivative
=11x2
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