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Differentiate tan^(-1)((2x)/(1-x^2))+cos...

Differentiate `tan^(-1)((2x)/(1-x^2))+cos^(-1)((1-x^2)/(1+x^2))` with respect to `x` , when `x in (-1,\ 0)`

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Given that,
`y=tan^(-1)((2x)/(1-x^2))+cos^(-1)((1-x^2)/(1+x^2))`
`x in (-1, 0)`.
`y=tan theta`
`y= tan^-1 [(2tantheta)/(1-tan^2 theta)]+cos^-1 [(1-tan^2theta)/(1+tan^2theta)]`
`=>y=tan^-1 (tan2theta)+cos^-1(cos2theta)`
`x in ( -1,0)`.
`=>tan theta in ( -1,0)`
`=>2theta in (-pi/2,0)`
`y=2theta-2theta`
`=>y=0`
`(dy)/(dx)=0`
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate tan^(-1)((2x)/(1-x^2))+cos^(-1)((1-x^2)/(1+x^2)) with re...

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  2. Differentiate tan^(-1)((2x)/(1-x^2))+cos^(-1)((1-x^2)/(1+x^2)) with re...

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  3. Differentiate tan^(-1)((2x)/(1-x^2))+cos^(-1)((1-x^2)/(1+x^2)) with re...

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  4. Differentiate tan^(-1)((2x)/(1-x^2))+cos^(-1)((1-x^2)/(1+x^2)) with re...

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  5. If y=sin^(-1)x+sin^(-1)sqrt(1-x^2) , find (dy)/(dx) in each of the fol...

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  6. Differentiate cos^(-1){2xsqrt(1-x^2)},1/(sqrt(2))lt x lt 1

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  7. Differentiate cos^(-1){sqrt((1+x)/2)}\ ,\ -1<x<1 with respect to x

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  8. Differentiate sin^(-1){sqrt((1-x^2)}\ ,\ \ 0<x<1 with respect to x

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  9. Differentiate sin^(-1){sqrt(1-x^2)},\ 0<x<1 with respect to x

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  10. Differentiate tan^(-1){x/(sqrt(a^2-x^2))}\ ,\ -a<x<a with respect to x

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  11. Differentiate sin^(-1){x/(sqrt(x^2+a^2))} with respect to x

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  12. Differentiate sin^(-1)(2x^2-1),\ \ 0<x<1 with respect to x

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  13. Differentiate sin^(-1)(1-2x^2),0ltxlt1 with respect to x

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  14. Differentiate cos^(-1){x/(sqrt(x^2+a^2))} with respect to x

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  15. Differentiate sin^(-1){(sinx+cosx)/(sqrt(2))},\ -(3pi)/4<x<pi/4 with r...

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  16. Differentiate cos^(-1){(cosx+sinx)/(sqrt(2))},\ -pi/4<x<pi/4 with resp...

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  17. Differentiate tan^(-1){x/(1+sqrt(1-x^2))},\ -1<x<1 with respect to x

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  18. Differentiate tan^(-1){x/(a+sqrt(a^2-x^2))},\ -a<x<a with respect to x

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

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  20. Differentiate cos^(-1){(x+sqrt(1-x^2))/(sqrt(2))},\ -1<x<1 with respec...

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