Question

Develop the formula for the derivative of \( arcsin x\)

Answer 1

y = ArcSin(x)
x = Sin(y)
implicit differentiation...

Answer 2

Pick it up from here

Answer 3

1*dx/dx = Cos(y)*dy/dx

Answer 4

1 = Cos(y)(dy/dx)
dy/dx = 1/Cos(y)

Answer 5

y = ArcSin(x), so
dy/dx = 1/Cos(ArcSin(x))

Answer 6

Alright, I think got it, thanks bah~

Answer 7

And now work some trig magic if you have to, I don't remember if this is actually the derivative

Answer 8

@bahrom7893 Can go harder.

Answer 9

One method that works for me is to transform y=arcsin x into the corresponding equation for the sine: sin y=x. All you need to do now is to find the derivative dy/dx using implicit differentiation and remembering the chain rule.