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Differentiate the following functions wi...

Differentiate the following functions with respect to `x` : (i) `tan^(-1){sqrt(1+x^2)-x}` , `x in RR` (ii) `tan^(-1){(sqrt(1+x^2)-1)/x},\ \ x!=0`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate tan^(-1)(secx+tanx) , -pi/2<x<pi/2 with respect to x :

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  2. Differentiate tan^(-1){sqrt(1+x^2)+x},\ x in RR with respect to x .

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  3. Differentiate the following functions with respect to x : (i) tan^(-1...

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  4. Differentiate the following functions with respect to x: (i) tan^(-1){...

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  5. Differentiate tan^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(...

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  6. Differentiate the following functions with respect to x tan^(-1)((a+...

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  7. Differentiate tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)),\ -1/(sqrt(3))<x/a<1/...

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  8. Differentiate tan^(-1)sqrt (a-x)/sqrt(a+x), -a < x < a

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  9. If y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2]) and 0 < x < 1, then find...

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  10. differentiate xtany=80

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  11. If y=tan^(-1){(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))} , -...

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  12. Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , with ...

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  13. Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , with ...

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  14. Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) , with ...

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  15. Differentiate sinxtanx with respect to x

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

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

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  18. Evaluateint(x+e^x)\dx

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

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

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