Thursday, January 8, 2009

Differentiate Inverse Sine (arcsin) - proof

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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