Home
Class 12
MATHS
If xsqrt(1 + y) + ysqrt(1 + x) = 0 x != ...

If `xsqrt(1 + y) + ysqrt(1 + x) = 0 x != y` prove that `(dy)/(dx) = (-1)/((1 + x)^(2))`

Promotional Banner

Similar Questions

Explore conceptually related problems

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

If x^(y) = e^(x - y) prove that (dy)/(dx) = (log_(e)x)/((1 + log_(e)x)^(2)) .

If y^(x) = e^(y -x) , prove that (dy)/(dx) = ((1 + log y)^2)/(log y) .

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

If x=sqrt(a^(sin^(-1)t)) then prove that (dy)/(dx)=(-y)/(x)

If y = sin(log_(e) x) prove that (dy)/(dx) = sqrt(1-y^2)/x

If e^(y)(x + 1) = 1 show that (d^2 y)/(dx^2) = ((dy)/(dx))^(2) .

x = sqrt(a^(sin^(-1)t)), y=sqrt(a^(cos^(-1)t)) , Prove that: (dy)/(dx) = -y/x