Home
Class 12
MATHS
If log (x^(2)+y^(2)) = 2 tan ^(-1) (x/y)...

If `log (x^(2)+y^(2)) = 2 tan ^(-1) (x/y) " then show that " (dy)/(dx) = (y-x)/(y +x)`

Text Solution

AI Generated Solution

To solve the problem, we need to differentiate the given equation and isolate \(\frac{dy}{dx}\). Let's go through the steps systematically. ### Step 1: Start with the given equation We have the equation: \[ \log(x^2 + y^2) = 2 \tan^{-1}\left(\frac{x}{y}\right) \] ...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Assignment ( section -A)|61 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Section -B|35 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise section - J|6 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

  • DETERMINANTS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J|12 Videos

Similar Questions

Explore conceptually related problems

If log (x^2+y^2)=2t a n^(-1)\ (y/x), then show that (dy)/(dx)=(x+y)/(x-y)

"If "log(x^(2)+y^(2))=2tan^(-1)""((y)/(x))," show that "(dy)/(dx)=(x+y)/(x-y)

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

If x=y log(xy) , then prove that (dy)/(dx) = (y (x-y))/(x(x+y)) .

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

If x^(y) y^(x)=5 , then show that (dy)/(dx)= -(log y + (y)/(x))/(log x + (x)/(y))

If log ((x^(2) -y^(2))/( x^(2)+ y^(2))) =a, Prove that (dy)/(dx) =(y)/(x).

(dy)/(dx)=(x+y+1)/(2x+2y+3)

If y=tan^(-1)x , show that (1+x^2)(d^2y)/(dx^2)+2x(dy)/(dx)=0 .

y^2+x^2(dy)/(dx)=x y(dy)/(dx)