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If y = tan^(-1)((1+x^(2))/(1-x^(2))) Fin...

If `y = tan^(-1)((1+x^(2))/(1-x^(2)))` Find `dy/dx`.

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The correct Answer is:
`(2x)/(1+x^(4))`
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(i)If y = x^(3) + x^(2) + x +1 then dy/dx at x = 1 is 0 (ii)If y=sin^(-1)((2x)/(1+x^(2))) then dy/dx = tanx (iii) y = x^(x) dy/dx = x^(x)[1+logx] (iv) y = tan^(-1)x, dy/dx = 1/(1 + x^(2) state which pair of the statement given above are true.

Find (dy)/(dx) in the following : y = tan^(-1)((3x-x^(3))/(1-3x^(2))), -(1)/(sqrt(3)) lt x lt (1)/(sqrt(3)) .

PREMIERS PUBLISHERS-DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION -PROBLEMS FOR PRACTICE
  1. y = sec^(-1)((1+x^(2))/(1-x^(2))), find dy/dx.

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  2. Find the derivatives of the following : tan^(-1)((cosx+sinx)/(cosx-s...

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  3. If y = tan^(-1)((1+x^(2))/(1-x^(2))) Find dy/dx.

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  4. y = tan^(-1)((sqrt(x)+sqrt(a))/(1-sqrt(ax))), find dy/dx.

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  5. y = tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))),find dy/dx.

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  6. y = cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))),...

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  7. Differentiate cosec^(-1)(1/(3x-4x^(3))):

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  8. If x=asec^(3)theta " and " y=atan^(3)theta " find " (dy)/(dx) " at " t...

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  9. If x = 2costheta- cos 2theta, y = 2sintheta -sin 2theta, find dy/dx.

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  10. x = a(costheta + logtan(theta/2), y = asintheta, find dy/dx.

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  11. If x^(m)y^(n) = (x+y)^(m+n),find dy/dx.

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  12. If e^(x)+ e^(y) = e^(x+y), find dy/dx.

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  13. If ax^(2) +2hxy + by^(2) + 2gx + 2fy + c = 0, find dy/dx.

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  14. If y = cos (m sin^(-1) x), prove that (1-x^2)y3 -3 xy2 + ( m^2 -1) y1=...

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  15. Differentiate tan^(-1)(2x/(1 - x^(2))) with respect to cos^(-1)((1 - x...

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  16. If y = sqrt((x-1)(x-2)(x-3)), find dy/dx.

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  17. Differentiate cosec^(-1)((1 + x^(2))/(2x)) with respect to cot^(-1)((1...

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  18. f(x)={(x,0,le,x,le,2),(3x,-,1,2,lt,x,le,3):} then f'(2^(+)) is:

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  19. f(x)={(x,0,le,x,le,1),(2x,-,1,1,lt,x,le,2):} then f'(1^(-)) is :

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  20. If f(x)=x^2 and is differentiable an [1,2] f'(c) at c where c in [1,2]...

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