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If -(1)/sqrt(3) lt x lt (1)/sqrt(3), th...

If `-(1)/sqrt(3) lt x lt (1)/sqrt(3), then tan^(-1) (3x-x^(3))/(1-3x^(2))` equals

A

`(3)/(1 + x^(2))`

B

`(1)/(1 + x^(2))`

C

`(-3)/(1 - x^(2))`

D

`(3)/(1 - x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Put ` x = tan theta `
` therefore y= tan^(-1) ((3x-x^(3))/(1 -3x^(2))) = tan^(-1) ((3 tantheta - tan^(3) theta )/(1 - 3 tan^(2) theta))`
` rArr y = tan^(-1) (tan 3 theta) = 3 theta = 3tan^(-1) x ` .
On differentiating both sides of Eq .(i) w.r.t.x, we get
`rArr (dy)/(dx) = 3 (d)/(dx) (tan^(-1) x) = (3)/(1 + x^(2))`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 DERIVATIVE OF INVERSE TRIGONOMETRIC FUNCTIONS (BY SUBSTITUTION)
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  2. If -(1)/sqrt(3) lt x lt (1)/sqrt(3), then tan^(-1) (3x-x^(3))/(1-3x^(...

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  3. If y = sin^(-1) ((1 -x^(2))/(1 +x^(2))),0 lt x lt 1 " then " (dy)/(dx...

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  4. Prove that : cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(...

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  5. Differentiate the functions with respect to x : cos^(-1){(cosx+sinx)/...

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  6. Derivative of sin^(-1) ((1)/(sqrt(x + 1))) with respect to x is

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  7. If sin^(-1)x+sin^(-1)y=pi/2, then dy/dx is equal to

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  8. (d)/(dx)[sin^(-1)(xsqrt(1 - x)- sqrt(x)sqrt(1 - x^(2)))] is equal to

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  9. If y = cos^(-1) ((2x)/(1 + x^(2))), - 1 lt x lt 1 " then " (dy)/(dx)...

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  10. If y = sin^(-1) x + sin^(-1) sqrt(1 - x^(2)), - 1 le x le 1," then " ...

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  11. If y = tan^(-1) (sec x - tan x ) , "then" (dy)/(dx) is equal to

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  12. d/(dx)[sin^2cot^(- 1)sqrt((1-x)/(1+x))] is

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  13. If y = tan^(-1) x + cot^(-1) x + sec^(-1) + "cosec"^(-1) x . "then" (...

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  14. If y = sin^(-1) sqrt(1-x), "then " (dy)/(dx) is equal to

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  15. If y = tan^(-1)((cos x)/(1 + sin x)), "then" (dy)/(dx) is equal to

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  16. If y = sin[cos^(-1){sin(cos^(-1) x)}], "then" (dy)/(dx)" at x" = (1)/...

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  17. If y = tan^(-1) sqrt((1-sinx)/(1+sinx)), then the value of (dy)/(dx...

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  18. The derivative of tan^(-1)((sqrt(1 + x)-sqrt(1-x))/(sqrt(1 + x)+sqrt(1...

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