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

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

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If the derivative of tan^(-1)(a+b x) takes the value 1 at x=0, prove t...

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  2. If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],find(dy)/(dx)

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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 = cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2), -1/2ltxlt0 , find (dy)/(dx...

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  5. If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),p rov et h a t(dy)/(dx)=(x^2)/(y...

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  6. If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1)a , prove that (dy)/(dx)=y/xd...

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  7. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0<x<1 (ii) -1<x...

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  8. Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , if -1/(sqrt(3))<x<1/(sqrt(...

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  9. Differentiate each of the following functions with respect to x : (...

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  10. Differentiate the following function with respect to x : sin^(-1)(si...

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  11. Differentiate sin^(-1)(2xsqrt(1-x^2))w i t hr e s p e c ttox ,if -1/(...

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  12. Differentiate sin^(-1)(3x-4x^3) with respect to x , if (i)-1/2ltxlt...

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  13. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0<x<1 (ii) -1<x...

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  14. If y=cos^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x^2)} and 0<x<1, find (dy)/(dx...

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

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  16. If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

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

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  18. If y=xsin^(-1)x+sqrt(1-x^2), p rov et h a t(dy)/(dx)=sin^(-1)x

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  19. If y=1/2log((1-cos2x)/(1+cos2x)),p rov et h a t(dy)/(dx)=2cos e c2x

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  20. If y=x e^x, find dy/dx

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