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Prove that d/(dx){x/2sqrt(a^2-x^2)+(a^2)...

Prove that `d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)}=sqrt(a^2-x^2)`

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Differentiate tan^(-1)(x/(sqrt(1-x^2))) with respect to sin^(-1)(2xsqrt(1-x^2)), if -1/(sqrt(2)) < x< 1 /(sqrt(2))

Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to tan^(-1)(x/(sqrt(1-x^2))) .

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=sqrt(a^2-x^2) , prove that y(dy)/(dx)+x=0

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  2. If x y=4 , prove that x((dy)/(dx)+y^2)=3y

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  3. Prove that d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a)}=sqrt(a^2-x^2)

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  4. Differentiate sin^(-1)(sinx),\ \ x in [0,\ 2pi]

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  5. Differentiate cos^(-1)(cosx),\ \ x in [0,\ 2pi]

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  6. Differentiate tan^(-1)(tanx),\ \ x in [0,\ pi]-{pi/2}

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  7. Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to x , if -1/(sqrt(...

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  8. Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to x , if 1/(sqrt(2...

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  9. Differentiate sin^(-1)(2xsqrt(1-x^2)) with respect to x ,

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  10. Differentiate sin^(-1)(3x-4x^3) with respect to x , if -1/2<x<1/2

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  11. Differentiate sin^(-1)(3x-4x^3) with respect to x , if 1/2<x<1

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  12. Differentiate sin^(-1)(3x-4x^3) with respect to x

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

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

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

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

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  17. Differentiate cos^(-1)(4x^3-3x) with respect to x , if x in (-1/2,1/2)

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  18. y=sec^(-1)""(1)/(2x^(2)-1),0ltxlt(1)/(sqrt(2))

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  19. Differentiate cos^(-1)(4x^3-3x) with respect to x , if x in (-1,\ -1/2...

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  20. Differentiate tan^(-1)((2x)/(1-x^2)) with respect to x , if x in (-1,\...

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