If `y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx)` is (a)`(n y)/(sqrt(x^2+a^2))` (b) `-(n y)/(sqrt(x^2+a^2))` (c)`(n x)/(sqrt(x^2+a^2))` (d) `-(n x)/(sqrt(x^2+a^2))`

If x y+y^2=tanx+y ,t h e n(dy)/(dx)dot

If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)) ,then (dy)/(dx) is equal to (a) (a y)/(xsqrt(a^2-x^2)) (b) (a y)/(sqrt(a^2-x^2)) (c) (a y)/(xsqrt(a^2-x^2)) (d) none of these

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) 1/(2xsqrt(x^2-1)) (d) none of these

If y=sqrt(log{sin((x^2)/3-1)}) , t h e n find (dy)/(dx)dot

If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to (a) (e^(sqrt(x)))/(2sqrt(x)) (b) (e^(sqrt(x))-e^(-sqrt(x)))/(2x) 1/(2sqrt(x))sqrt(y^2-4) (d) 1/(2sqrt(x))sqrt(y^2+4)

x dy - y dx = sqrt(x^(2) + y^(2)) dx

Given y=(5x)/(3sqrt((1-x)^2 ))+sin^2(2x+1), (dy)/(dx)

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to x/y (b) y/(x^2) (x^2-y^2)/(x^2+y^2) (d) y/x