Let x=siny find dy/dx in terms of x? is 1/cos(arcsinx) wrong ?

Question

Let x=siny find dy/dx in terms of x? is 1/cos(arcsinx) wrong ?

Answer 1

y=arcsin(x)

dy/dx=d(arcsin(x))/dx=1/sqrt(1-x^2)

Answer 2

1 = cos(y) dy/dx

dy/dx = 1/cos(y)

x = sin(y)

1 - sin^2(y) = cos^2(y) = 1 - x^2

cos(y) = SQRT(1 - x^2)

dy/dx = 1/SQRT(1 - x^2)

Your answer is right though probably not the best way to express it.

Answer 3

1 = (cosy) (y')

=> y' = 1/cosy

but y = arcsinx

hence y' = 1/cos(arcsinx)