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

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

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If x^3+y^3+3a x y=0 , f i n d dy / dx

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  2. If 1 is the twice repeated root of the equation a x^3+b x^2+b x+d=0,t ...

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

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  4. If y=btan^(-1)(x/a+tan^(-1)y/x),find(dy)/(dx)dot

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  5. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to (a)1/(2y-1)...

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  6. If y=sqrt(sinx+y), then find (dy)/(dx)

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  7. f(x)=|x^2-3|x|+2|dot Then which of the following is/are true f^(prime)...

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

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  9. If x^3-2x^2y^2+5x+y-5=0 and y(1)=1, then (a)y^(prime)(1)=4/3 (b) y...

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  10. If x^y=e^(x-y), Prove that (dy)/(dx)=(logx)/((1+logx)^2)

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  11. Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1)xdot Then (a)f^(prime)(10...

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  12. If sqrt(x) +sqrt(y)=4, f i n d (dx/dy) a t (y = 1).

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  13. If y=(x^4-x^2+1)/(x^2+sqrt(3)x+1) and (dy)/(dx)=a x+b , then the value...

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  14. If x y+y^2=tanx+y ,then find (dy)/(dx)

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  15. Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e...

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  16. If y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+oo)))),t h e np rov et h a t(dy)/(dx)...

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  17. If y=x^((logx)^("log"(logdotx))),t h e n(dy)/(dx)i s (a)y/x(1n x^(x-...

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  18. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)=(c...

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  19. The n t h derivative of x e^x vanishes when (a)x=0 (b) x=-1 (c)...

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  20. If x=a(cost+1/2logtan^2t) and y=asint then find (dy)/(dx) at t=pi/4

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