Question

diffrential formula for inverse trigonometry function ​

Answer 1

Derivatives of Inverse Trigonometric Functions. (arcsinx)′=f′(x)=1φ′(y)=1(siny)′=1cosy=1√1−sin2y=1√1−sin2(arcsinx)=1√1−x2(−1<x<1). (arcsec x)′=1(secy)′=1tanysecy=1secy√sec2y−1=1|x|√x2−1. ... (arccsc x)′=1(cscy)′=−1cotycscy=−1cscy√csc2y−1=−1|x|√x2−1