How do you differentiate x+siny=0 with respect to x?

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Answer 1 · 2017-03-08T03:59:44

#(d y)/(d x) = -1/(sqrt (1-x^2))#

#x + sin y = 0#
#sin y = -x#
#y = sin^(-1) (-x)#

let say # u = -x#,
#(d u)/(d x) = -1#

therefore,

#y = sin^(-1) u#
#(d y)/(d x) = 1/(sqrt (1-u^2)) * (du)/(dx)#

#(d y)/(d x) = 1/(sqrt (1-(-x)^2)) * (-1)#

#(d y)/(d x) = -1/(sqrt (1-x^2))#