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Answer 1 · 2015-11-08T00:02:38

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

Simply find #dy/dx# first

Using product rule we find the following
#dy/dx = x *(sqrt(1-x^2))' + (sqrt(1-x^2))(x)'#

#dy/dx = x *(sqrt(1-x^2))' + (sqrt(1-x^2))1#

#dy/dx = x *((-2x)/(2sqrt(1-x^2))) + sqrt(1-x^2)#

#dy/dx = (-x^2)/(sqrt(1-x^2)) + sqrt(1-x^2)#

#dy/dx = (-x^2)/(sqrt(1-x^2)) + (1-x^2)/sqrt(1-x^2)#

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

now just multiply the #dx# to the other side

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