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Prove that, If y = Sin -1 x, x ∈ (–1, 1) then dy/dx =1/√(1-x 2)

Prove that, If y = Sin-1 x, x ∈ (–1, 1) then dy/dx =1/√(1-x2)

Grade:12th pass

2 Answers

RAJU
398 Points
5 years ago
y = Sin-1x ⇒ x = sin y
dy/dx=cosy
dy/dx=(dx/dy)-1
=1/cosy=1/√(1-sin2y)
=1/√(1-x2)
 
Raghu Vamshi Hemadri
72 Points
5 years ago
 
y = Sin-1x ⇒ x = sin y
dy/dx=cosy
dy/dx=(dx/dy)-1
=1/cosy=1/√(1-sin2y)
=1/√(1-x2)
 

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