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If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1...

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

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To prove that \(\frac{dy}{dx} = \frac{y}{x}\) given the equation \[ \cos^{-1}\left(\frac{x^2 - y^2}{x^2 + y^2}\right) = \tan^{-1}(a), \] we will follow these steps: ...
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If cos^(-1)((x^(2)-y^(2))/(x^(2)+y^(2)))=tan^(-1)a , prove than (dy)/(dx)=(y)/(x).

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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2),-1/2<x<0 , find (dy)/(dx)

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

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

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

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  5. Differentiate tan^(-1)((3x-x^3)/(1-3x^2)),if -1/sqrt(3)ltxlt1 /sqrt...

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  6. Differentiate each of the following functions with respect to x : (i)...

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

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

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  9. Differentiate sin^(-1)(3x-4x^3)

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

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

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

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

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

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

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

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  17. If y=e^xcosx ,p rov et h a t(dy)/(dx)=sqrt(2)e^xcos(x+pi/4)

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  18. If y=(x-1)log(x-1)-(x+1)log(x+1),p rov et h a t(dy)/(dx)=log((x-1)/(1+...

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  19. If y=sqrt(x)+1/(sqrt(x)),p rov et h a t2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))

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  20. P rov et h a t d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)x/a}=sqrt(a^2-x^...

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