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If y = sqrt((1+x)/(1-x)), prove that (1-...

If `y = sqrt((1+x)/(1-x))`, prove that `(1-x^2) dy/dx - y = 0`

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Differentiate the following functions w.r.t.x : (5x)^(3cos^2x)

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  2. If y = sin (cos sqrtax + b), find dy/dx

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  3. If y = sqrt((1+x)/(1-x)), prove that (1-x^2) dy/dx - y = 0

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  4. If y = sqrt((1-sin2x)/(1+sin2x)), prove that dy/dx + sec^2 (pi/4 -x) =...

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  5. If y = e^(x + 3 log x) prove that dy/dx = x^2 (x+3) e^x

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  6. If y = (e^x + e^-x)/(e^x - e^-x), then show that (dy/dx) = 1 - y^2

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  7. Find the derivatives of the following functions at the indicated point...

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  8. Find the derivatives of the following functions at the indicated point...

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  9. Find the derivatives of the following functions at the indicated point...

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  10. Find the derivatives of the following functions at the indicated point...

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  11. Find the derivatives of the following functions at the indicated point...

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  12. Find the derivatives of the following functions at the indicated point...

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  13. Find dy/dx when x = t + 1/t, y = t - 1/t

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  14. Find dy/dx, when: x = e^(theta) ( theta+1/theta) and y = e^(-theta)(th...

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  15. Find dy/dx when x = a sin^2 t, y = b cos^2 t

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  16. Find dy/dx when x = e^(t-sint), y = e^(t + cost)

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  17. Find dy/dx when x= a cos^3 t , y = b sin^3 t

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  18. Find dy/dx when x = e^t (sin t + cos t), y = e^t (sin t - cos t)

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  19. Find dy/dx when x = cos theta + cos 2 theta, y = sin theta + sin 2 the...

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  20. Find dy/dx when x= a (theta + sin theta), y = a(1+cos theta)

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