Need help deriving this equation

derive y=sin^-1 (1/x)

please explain step by step. the answer should be -1/|x|√(x^2-1)
thanks :)

The correct word is "differentiate (with respect to x)"
Did your teacher not teach you the terminology?

You need to use implicit differentiation.
Basically you treat the function as an equation and manipulate it so it's easier to differentiate. Then you take the derivative of both sides using the chain rule and express the derivative of y as a variable (y')
You then solve for the variable to get your answer.

y = arcsin(1/x)
[ Note: arcsin = sin^(-1) ]

sin(y) = 1/x
d/dx (sin(y)) = d/dx (1/x)
y' cos(y) = -1/x^2
y' = (-1/x^2 ) / cos(y) = -1/ (x^2*cos(arcsin(1/x)))

Now we just need to simplify cos(arcsin(1/x)) into something more elegant:
Draw a right triangle labeling one leg 1, and the hypotenuse x.
Sine is opposite over hypotenuse, so the sine of the angle opposite of that leg must be 1/x
That angle is y.
Cosine is adjacent over hypotenuse. you know the hypotenuse is x, but the adjacent must be calculated using the Pythagorean theorem: adjacent = sqrt(x^2-1)
So cos(y) = sqrt(x^2-1) / x

Plugging that into -1/ (x^2*cos(y)) yields:
-1 / (x^2*sqrt(x^2-1)/x)
Clearly the x in the denominator can cancel out one of the x in x^2, but note that x^2 is always positive while x isn't. That is why you need to add the absolute value:
-1 / (|x|*sqrt(x^2-1)) <= Final Answer

Edit:
BTW Wolfram Alpha is also correct; they just avoided the absolute value:
Wolfram Alpha says:
-1 / (x^2*sqrt(1-1/x^2))

They basically changed sqrt(x^2-1) / x into
sqrt(x^2-1) / sqrt(x^2) = sqrt( (x^2-1) / x^2) = sqrt(1-1/x^2)

http://www.wolframalpha.com/input/?i=sin…


its got your answer there

just click show steps.

no but theres a ans w/ app is it applied-ing to ? ie as mass