" i) Prove "(1)/(sqrt(|x|-x))" exist when "x<0

Prove (1)/(sqrt(|x|-x)) exists when x<0

Prove 1/(sqrt(|x|-x)) exists when x < 0

y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)] prove tha t dy/dx is (1)/(2sqrt(x(1-x)))

If y = sqrt(x) + (1)/(sqrt(x)) prove that 2x(dy)/(dx) + y = 2sqrt(x)

If y=tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))] then prove that (dy)/(dx)=(1)/(2sqrt(1-x^(2)))

If sqrt(x) + sqrt(y) = sqrt(5) , Prove that (dy)/(dx) = (-3)/(2) when x= 4" and "y=9 .

if y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)] then prove that (1)/(2sqrt(x)sqrt(1-x))

lim_(x rarr1)(sqrt(1-cos2(x-1)))/(x-1) a.exists and its equals sqrt(2) b.exists and its equals sqrt(-2) c.does not exist because x-1rarr0 d.L.H.L. not equal R.H.L.

If y=sqrt(x)+1/(sqrt(x)) , prove that 2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))