Home
Class 12
MATHS
"If "xsqrt(1+y)+ysqrt(1+x)=0," prove tha...

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

Text Solution

AI Generated Solution

To solve the given problem, we start with the equation: \[ x\sqrt{1+y} + y\sqrt{1+x} = 0 \] ### Step 1: Rearranging the Equation We can rearrange the equation to isolate one of the terms: \[ x\sqrt{1+y} = -y\sqrt{1+x} \] ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.3|10 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.4|12 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Concept Application 3.1|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • DOT PRODUCT

    CENGAGE ENGLISH|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If x sqrt ( 1+ y) + y sqrt( 1+x) =0 , prove that (dy)/( dx) = - (1)/( (1+x)^2) .

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

If ysqrt(1-x^2)+xsqrt(1-y^2)=1," prove that "(dy)/(dx)= - sqrt((1-y^2)/(1-x^2))dot

If x y=1 , prove that (dy)/(dx)+y^2=0 .

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

If y=sqrt((1-x)/(1+x)), prove that (1-x^2)dy/(dx)+y=0

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

xsqrt(1+y)+ysqrt(1+x)=0 then (dy)/(dx)=

If y=sqrt((1-x)/(1+x)), prove that ((1-x^2)dy)/(dx)+y=0

If y=sqrt((1-x)/(1+x)) prove that (1-x^2)(dy)/(dx)+y=0