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If 1/2 (e^y - e^-y) = x, prove that : dy...

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

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Find dy/dx if y=x^x

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  2. Find dy/dx when: xy + ce^-y + ye^x = x^2

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

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  4. If xy = e^(x - y), prove that (dy)/(dx) = (y (x - 1))/(x (y + 1))

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  5. If y = (sin^-1x)/(sqrt(1-x^2)), prove that (1-x^2)(dy/dx)- xy = 1

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  6. If x=tan((1)/(2)logy), then show that (1+x^(2))(d^(2)y)/(dx^(2))=(a-2x...

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  7. Differentiate tan^-1((2^(x+1))/(1-4^x)) with respect to x.

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  8. If y = log10 sin x, prove that dy/dx=(log10 e) cotx

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  9. If y = sin[sin(log3x)]. Find dy/dx

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  10. Find, from first principle , the derivative of the following w.r.t. x:...

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  11. Find, from first principle , the derivative of the following w.r.t. x:...

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  12. Differentiate the following w.r.t. x: e^-x

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  13. Find, from first principle , the derivative of the following w.r.t. x:...

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  14. Find, from first principle , the derivative of the following w.r.t. x:...

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  15. Find, from first principle , the derivative of the following w.r.t. x:...

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  16. Find, from first principle , the derivative of the following w.r.t. x:...

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  17. Find, from first principle , the derivative of the following w.r.t. x:...

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  18. Find, from first principle , the derivative of the following w.r.t. x:...

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  19. Find dy/dx, if x and y are connected parametrically by the equations, ...

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  20. Find dy/dx, if x and y are connected parametrically by the equations, ...

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