Question

find dy/dx for the equation xsiny=1

Answer 1

@song6 I am sorry, I am not with you then. :)

Answer 2

xsiny=1--> siny = 1/x--> y = arcsin(1/x), then take derivative and apply chain rule to get y' = (arcsin(1/x)' = we have formula to get this derivative, right??

Answer 3

x siny=1
\[siny=\frac{ 1 }{ x }\]
\[cosy \frac{ dy }{ dx }= \frac{ -1 }{ x ^{2} }\]

Answer 4

At the end, you still have cos y which is unknown. How?? You must find out y' w.r.t x only.

Answer 5

\[y' = (arcsin(1/x)' = \dfrac{1}{\sqrt{1-(1/x)^2}}*(1/x)'=-\dfrac{1}{x^2\sqrt{1-1/x^2)}}\]

Answer 6

y' totally respects to x, you don't have any y from the right hand side.

Answer 7

um ...wait for a second

Answer 8

http://www.wolframalpha.com/input/?i=%28arcsin%281%2Fx%29%29%27