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"tan"^(-1)(x)/(sqrt(a^(2)-x^(2)))...

`"tan"^(-1)(x)/(sqrt(a^(2)-x^(2)))`

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The correct Answer is:
`1/(sqrt(a^(2)-x^(2)))`
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The simplest form of tan^(-1)((x)/(a+sqrt(a^(2)-x^(2)))) is :

Prove that tan^(-1){(x)/(a+sqrt(a^(2)-x^(2)))}=(1)/(2)(sin^(-1)x)/(a),-a

Prove that tan^(-1) {(x)/(a + sqrt(a^(2) - x^(2)))} = (1)/(2) sin^(-1).(x)/(a), -a lt x lt a

Differentiate tan^(-1)(x)/(1+sqrt((1-x^(2))))+{2tan^(-1)sqrt(((1-x)/(1+x)))}sin w.r.t.x

Differentiate the following w.r.t. x : tan^(-1)((sqrt(1+a^(2)x^(2))-1)/(ax))

prove that tan^(-1)((x)/(1+sqrt(1-x^(2)))]=(1)/(2)sin^(-1)x

Differentiate the functions with respect to x:tan^(-1){(sqrt(1+a^(2)x^(2))-1)/(ax)},x!=0

Find (dy)/(dx) when (y-tan^(-1))(x)/(1+sqrt(1-x^(2)))+sin[2tan^(-1)sqrt((1-x)/(1+x))]

y=tan^(-1)((x)/(1+sqrt(1-x^(2))))+sin(2tan^(-1)theta*sqrt((1-x)/(1+x))) then prove that ,4(1-x^(2))^(3)((d^(2)y)/(dx^(2)))^(2)+4x=x^(2)+4

Differentiate the following function with respect to x:tan^(-1){(sqrt(1+a^(2)x^(2))-1)/(ax)},x!=0

MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(e) (SHORT ANSWER TYPE QUESTIONS)
  1. Differentiate the following w.r.t. x : xsec^(-1)x.

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  2. Differentiate the following w.r.t. x : cos^(-1)(sinx)

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  3. Differentiate the following w.r.t. x: (i)sin^(-1)2x" "(ii)tan^(-...

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  4. Differentiate the following w.r.t. x : (cot^(-1)x)^(2)

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  5. Differentiate the following w.r.t. x : sin(2sin^(-1)x)

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  6. Find the derivatives w.r.t. x : tan^(-1)((sinx)/(1+cosx))

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  7. "Tan"^(-1)(cosx)/(1+sinx)=

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  8. cot^(-1)((1+cosx)/(sinx))

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  9. Differentiate the following w.r.t. x : sin^(-1)(1-2x^(2))

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  10. sin^(-1)(3x-4x^(3))

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  11. Differentiate the following w.r.t. x : cos^(-1)(4x^(3)-3x),-1ltxlt1

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  12. Differentiate the following w.r.t. x : sin^(-1)((2x)/(1+x^(2))),-1lt...

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  13. "cosec"^(-1)((1+x^(2))/(2x))

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  14. Differentiate the following w.r.t. x : sin^(-1)((1-x^(2))/(1+x^(2)))...

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  15. Differentiate the following w.r.t. x : cos^(-1)((1-x^(2))/(1+x^(2)))...

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  16. Differentiate the following w.r.t. x : cos^(-1)((2x)/(1+x^(2))),-1lt...

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  17. Differentiate the following w.r.t. x : tan^(-1)((2x)/(1-x^(2))),0ltx...

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  18. tan^(-1)((3x-x^(3))/(1-3x^(2)))

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  19. निम्न फलन का x के सापेक्ष अवकल गुणांक ज्ञात कीजिए - tan ^(-1) [(x^(1/...

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  20. "tan"^(-1)(x)/(sqrt(a^(2)-x^(2)))

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