How to differentiate cos-1x
y=cos-1x
Bring the cos across
cosy = x
Differentiate both sides, remember when differentiating y time by dy/dx
-sin(y) dy/dx = 1
dy/dx = -1/siny
However we want to get the differential in terms of x, to do this we can use the identity
sin2t+cos2t = 1
so
sint = √(1 - cos2t)
putting this into our expression for dy/dx we get
dy/dx = 1/√(1-cos2y)
but cosy = x so
dy/dx = 1/√(1-x2)
by David Woodford
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