14.y=sin-1 (2xyl_x2V2 2
The given equation is y = sin − 1 ( 2 x 1 − x 2 )
y = sin − 1 ( 2 x 1 − x 2 ) `(1)
Let x = sin θ θ = sin − 1 x
Substitute sin θ for x in (1).
y = sin − 1 ( 2 sin θ 1 − sin 2 θ ) = sin − 1 ( 2 sin θ cos θ ) = sin − 1 ( sin ( 2 θ ) ) = 2 θ
Hence, y = 2 sin − 1 x
Differentiate both sides,
d y d x = 2 1 − x 2
Thus, derivative of sin − 1 ( 2 x 1 − x 2 ) is 2 1 − x 2 .
The given equation is
Let
Substitute
Hence,
Differentiate both sides,
Thus, derivative of
